It's a drop in a bucket. Global warming is due to ~5e18 Wh of excess heating. A nuke dumping 5e12 Wh of additional heat into water makes no difference at all.
Drops add up, just like using gas, oil, coal...
No, they really don't in this case. IIRC a sustained gigawatt of output over a 24 hour period is roughly equivalent to the sunlight absorbed by a 5 square kilometer patch of ocean in the tropics over the same period of time. The oceans absorb an almost incomprehensible amount of solar energy on a daily basis.