The Power Generation Information You Have Been Looking For Below
How do nuclear submarines avoid heat trails from power generation?
Do they stay in deep, colder water so it dissipates quickly?
First two answers: Wrong!
Subs simply rely on the massiveness of the heat sink the ocean is. The amount of heat a sub rejects is small compared to the amount that the surrounding water is able to absorb without significant temperature rise. Of course the seawater discharged is at an elevated temperature but that soon mixes with the ambient water (turbulence around the discharge points helps) and that equalizes down below the limit of detectability.