Here are some partial answers to your questions, to the best of my knowledge. Note that I did not do any testing and these answers are based on my overall experience in-game.
Regarding modules, you need to choose those that have the lowest power draw, as more power draw generate more heat. Usually, low class (small modules) and lower grade (E-D-C...) means less power draw, thus less heat.
The only exception to this rule that I know off is the "POWER PLANT" module. The power plant has a heat efficiency factor (%) which is smaller with better grade. What this means is that heat generated by your ship will be reduced by this factor. So even if the high grade power plant has more power draw than a lesser grade one, the lower heat factor will tip the scales for itself and the other modules.
On top of power draw, some modules like the Frame shift drive and thermal weapons have a thermal load, which means they generate additionnal heat when used.
If a module has a power draw, it produces heat. Therefore, a module like the cargo rack, which has no power draw, will not produce heat.
Simply put, if your only goal is to fly over a long period of time while producing the less possible heat, you want a ship with the lowest class (smallest in size) and lowest grade modules, except the best grade power plant. Also turn off all modules which you don't need while you're flying.
Regarding you're last question, I've heard different ships have different heat capacity and cooling speed, but I didn't test it myself and neither have I verified my sources. This one would remain to be answered.