Any reason WHY comets develop comas that far from the sun, considering the intensity of radiation/light that far out is about:

(Sun's energy output)
--------------------------
4 * Pi * R^2

or

(at 400,000,000 miles)

(Sun's energy output)
--------------------------
2,010,617,600,000,000,000

versus

(at 93,000,000 miles)

(Sun's energy output)
--------------------------
108,686,447,640,000,000

Let's just throw out a random large number and say the sun's output is 10^20 units per second.

At 400,000,000 miles, an object 1 square mile would be getting about 49.74 units per second of energy.

At 93,000,000 miles, the same object would be getting about 920.0779 units per second of energy. (I know the numbers are off by a lot and the units are exactly specified. But it's basically about 5% of the energy around Jupiter that we get at the earth.)
So, why do comets start outgassing there? It seems downright cold out there by comparison. Is there any way that enough energy would be getting to the surface let alone the interior of the comet/asteroid for it to start "outgassing?" How cold would the surface and interior of the comet be out at Jupiter's orbit? And is that sufficient temperature for the predicted "outgassing" that would seem to need a rather balmy environment to even be feasible?

I guess I'm asking that based strictly on an intensity-at-distance model (unless there's major other components for heating?) between the sun and other bodies. Do comets' "temperatures" assuming comas are sublimating gases, match what we'd predict for an object at said distance. Or do we predict that objects would be colder, and thus we should be surprised that object form comas out that far?

Hopefully the roundabout post/question made sense? Would 5% of the energy we receive at Earth be sufficient to raise the temperature of predicted icy gases on a comet sufficiently to their sublimation point? Or do we expect them to be too cold at that distance for out-gassing? & I guess, how do we know how hot something will be at a particular distance based on the sun's energy output and barring internal energy souce(s) in the object itself?

Guess, I'm just catching up to speed... :)