So, let me dumb it down for myself: Basically, you're saying nuclear energy causes global warming, due to leaking heat from the reactors. Is that correct?

If so, I think you're underestimating two things.

One, the amount of nuclear reactors on the planet. There's actually not that many in existence, in this day and age or any other (currently, there's around 436 active reactors worldwide). Even if they all simultaneously had a meltdown, it wouldn't raise global, let alone local temperatures a lick.

Which brings me to point two: insulation ability. Thermal energy is basically moving matter. The faster it's moving around on an atomic scale, the hotter it is (except for "wind chill" which still makes no sense to me, but hey). Most materials in general are generally good at preventing heat from transferring from nearby sources; thermal conductors aren't that common in nature last time I checked. The stuff they layer reactors with? Lead and concrete, pure and simple. It's dense, not very thermally-conductive, and the more you pile on, the less likely anything's going to affect you (If it wasn't that effective, reactor workers would be dead from radiation before they knew it). Notwithstanding they vast amounts of water they use to cool the reactors, the blanket of air that covers the planet probably also makes a pretty good thermal insulator.

And if you are feeling slightly warmer around a reactor, chances are you're probably seeing blue light too, in which case, you're pretty much screwed.

I could be wrong here in my thoughts on what you're saying here though. If I misinterpreted anything, let me know.