Seeings how you've got a nearly 'critial mass' of some nuclear material in some physical proximity, and seeings how nuclar reactions are taking place in this mass, releasing among other things, heat, what is the at rest, terminal temperature said nuclear mass reaches while mounted within whatever framework or container it is mounted? Also take into consideration whatever 'outer container' (such as a suitcase or foot locker) will do insofar as reducing the direct convection cooling that exposure to air open air would normally provide ...
You had some good questions about nukes. Here's the short version answer.
First: All of the following is unclassified information, easily available to those who take the time to learn about it.
You asked about heat: You don't start generating enough heat to matter until you get near a critical mass. To keep this from happening, you divide your fissionable material into at least two masses, separated by enough distance/shielding that a chain reaction cannot start. It is when you bring them together (rapidly!) that you reach critical mass and it blows up.
The suitcase nuke diagrams released by Congress were the simple "gun" type weapon (unclassified material). One mass is in the shape of a donut. The other is the shape of the "hole" in the donut. The "hole" is inside a tube ("gun") with an explosive charge at the end of the tube. When the explosive is fired the "hole" goes into the "donut", critical mass is reached, and it blows up.
Amazingly enough, the Internet used to have enough detailed information to build one of these. I don't know if it still does, but I checked once a few years ago and found everything I would have needed to know.
The trick is to get as much of the fissionable material to actually split as possible before the heat drives the critical mass apart. THAT little tidbit takes a lot of math plus precision explosives. If you don't get it right you will have a very "inefficient" bomb.
Unfortunately, lots of people have the required knowledge. And, even if the device turns out to be very inefficient, the odds are you will still get at least a small nuclear explosion. Worst case: It blows itself apart too soon and "all" you get is a dirty bomb. The psychological effect would still be huge.