I think that Jonah is overanalyzing the situation:

Also, I have another peeve. Aside from the talking bears living in a nice middle class house, doesn't the story defy the laws of nature? If the Papa bear's porridge is too hot, that logically should be because it's the biggest bowl and therefore would take the longest time to cool. The mama bear's porridge should be "just right" because it's the medium-sized one and the baby-bear's should be too cool. Or, as is so often the case, do I have my physics wrong?

One overanalysis deserves another. He's basically got it right, but it depends on the shape of the bowls. For any given shape, the larger the blob of porridge, the longer it will take to cool, because of the square-cube law. The volume of the porridge (which represents its heat capacity) goes up as the cube of the critical dimension (e.g., a diameter for a sphere) whereas the surface area (which is directly proportional to how fast it loses heat) goes up as the square.

For example, a cube of porridge an inch on a side will be one cubic inch of hot porridge that is cooled by six square inches of sides (assuming it's floating in, say, a space station, and can have all six sides exposed to air). A two-inch cube has eight cubic inches (eight times as much) of hot porridge, but only twenty-four square inches of cooling surface (six sides of four square inches, that is, only four times as much). So if you double the size of the critical dimension, you double the cooling time as well.

Of course, if you have a spherical blob of porridge, and a large thin pancake of it, you could have a larger amount of porridge that cooled faster in the latter case. If, for example, we took the eight cubic inches from the previous example, and spread it out to an eighth of an inch thin in a pancake shape, then you'd have something with sixty-four square inches on each side (a hundred twenty eight) plus the side area (an eighth times the circumference, which would be the square root of 64 divided by pi times 2pi, or 2 times the root of 64, or about two square inches). So now we have eight times the volume of the one-inch cube, but over twenty times the surface area, so it would cool much faster.

So if Momma Bear's porridge was in a wide flat bowl, and Baby Bear's in a higher, narrower one (perhaps with a picture of a Teddy Human on it), it's certainly conceivable hers could be colder than the baby's.

Porridge and bears aside, this is the principle employed when one pours hot tea into a saucer to cool it (the metaphorical function of the Senate, in the Founders' estimation, which would temper the urges of the House).

Why yes, I am in fact avoiding writing a proposal that's due next week. Why do you ask?

[Update mid afternoon]

Welcome, Corner readers. Just curious, though, why no comments from any of you? No one in the comments section except the regulars, so far. Does this say anything about Corner readers?

'Course the temp of real porridge depends on how much milk you've poured over it after putting it in the bowl. Clearly Mama Bear loves her milk.

Don't complicate things, Karl.

The entire analysis assumes that the porridge is ladled from the same part of the tureen. Clearly the uppermost layers of porridge are cooler than the lower layers, closer to the heat.

You're assuming that the stove hasn't been turned off prior to ladling. Though the upper layers will be cooler simply because they're closer to the top surface that cools. It also assumes that the ladlings occur simultaneously. Also, we have to factor in how long it took between tastings by Goldilocks. It could be that Baby Bear's was actually hottest at first, but that in the time it took her to get to it after trying the other two bowls, it cooled off. It's a very dynamic situation.

You also need to take into account the specific heat of the bowl that each bear had, and the initial temperature of the bowl (assume room temperature, I suppose), aside from the shape of the bowl. Specifically to be able to take into account the difference in heat loss among the various surfaces of the surface area of the porridge (quicker heat loss on the top surface exposed to air, compared to the surface in contact with the bowl). A wide flat bowl, made of kiln-dried clay, would probably contribute less to the cooling of the porridge than a deep bowl made of thin metal.

Which brings me to a question I ask every spring... Why doesn't anyone knock down and spread out large piles of snow in parking lots once the spring thaw comes? Why do they leave them piled up in a corner so that they take until May or June to melt?

Why doesn't anyone knock down and spread out large piles of snow in parking lots once the spring thaw comes?

Among other reasons, because by the time spring rolls around, those piles of snow are often piles of rock-like ice. Also, the whole point of gathering it up into those piles was to get it off the parking lot and streets, so people could drive safely.

I'm from the Corner, and I'm here to help you.... (Not really; I just wanted to congratulate you on performing so crucial an analysis. Any thoughts on the physics of changing clothes in a phone booth?)

Once it's 60 degrees on a daily basis, and doesn't drop below freezing at night, there's little harm in taking a yard of snow and spreading it out on a black parking lot for it to melt and/or sublimate, in my opinion. Then again, it would cost money...

I'm one of those strange people that enjoys shovelling snow in the winter, and then enjoys using physics to help get rid of it in the spring, though...

Don't forget to take into account the thermal conductivity of the bowls themselves, Papa might like his big, heavy ceramic bowl, Mama could be using a stainless one, and Baby is most likely using a thick walled and unbreakable plastic one.

Not just thermal conductivity of the bowls, but thermal capacity as well.

No no no.

Momma bear is on a diet, and she's only allowed 1400 calories per day. She's saving them for dinner, so she has a very small portion in a very large bowl that cooled off very quickly.

Or, perhaps papa bear simply served mama bear her porridge first. While papa bear's porridge was served later and thus had less time to cool ...

George, is Mama Bear on one of those calorie restriction life extension diets?

Actually, I think Kevin is onto something here. Papa made the porridge, but he's a lousy cook, so Mama only took a little to be polite, allowing hers to cool more quickly.

In related news, I hear that the bears in Spain are not hibernating any more because the weather is so warm in the winter these days. If you believe the old short story, the bears will start inventing things and discovering fire and stuff, since typically they forget everything when they hibernate.

Okay, I looked it up. "Bears Discover Fire" by Terry Bisson.

Not only do you ignore milk content and ladelling time, you also dont consider whether babys bowl has a different thermal conductivity to mama and papa bear's bowl. Those kiddie utensils quite often are made out of different sorts of plastics.

Bad science Rand, really bad science.

Papa Bear's bowl contains special "black body" porridge that will require years to cool to an edible temperature.

It seems to me that there is an undiscussed rule of science/human nature here. In my observations, once there is a baby in the house, it becomes a statistical impossibility for both parents to eat a hot meal. And there's a better that 75% chance that it will be the Momma bear who gets the cold meal. As to Pappa bear's being too hot, has anyone determined if there's a microwave in the cottage? That's a typical symptom when a grumpy Pappa bear complains about the food temperature, and a busy Momma bear leaves it in for too long.

The author wrote:

"Why yes, I am in fact avoiding writing a proposal that's due next week. Why do you ask?"

LOL

(I'm from the corner. Does this count as a comment?)
:-)