A piston soak is when you remove the spark plugs and pour a little bit of fuel injector cleaner or other chemical down the spark plug holes. Then you let it soak over night. The next day you will have to blow out the remaining chemicals before reinstalling the plugs and starting it up. Then an oil change is recommended too because some of the solution will end up in the oil.
In vague terms, heat soak simply refers to some part of the engine – or the engine as a whole – getting too hot. Combustion engines produce a lot of heat and that heat has to go somewhere. It soaks into metals and fluids. Eventually, it becomes so hot that heat absorption drops, and the engine can no longer efficiently rid itself of excess heat.