Space is a vacuum, and convection and conduction doesn't work. As an object heats up, it glows with light from the heat. The temperature determines the frequency. The earth is not a red-hot poker or a lake of lava, at its low temperature it glows feebly in the thermal infrared. This is how the excess heat is removed. Look up Planck's Law.

The hotter something gets, the more it glows, so sooner or later the heat escaping through radiation exactly equals the heat created by incoming sunlight, the heat from earth's core, and the sum total of human activity. The earth's atmosphere, and greenhouse gases in the atmosphere in particular, make the radiation harder to escape, so the earth gets hotter, emits even more, and eventually reaches equilibrium with the blackness of space at some higher temperature.

The point is, where does this incoming heat come from that must be disposed of? The vast majority comes from the sun. The heat produced by all our industrial activities, including power generation from fossil fuels AND nukes, is trivial in comparison. And the heat produced by residual radiation from our nukes is insignificant to THAT.

The sun provides approximately a Kilowatt per square meter at the top of the atmosphere, all human thermal activities on the planet are insignificant when compared to that. A very big thousand megawatt thermoelectric steam plant (whether nuclear or coal fired) produces as much total energy as 10^6 m^2, or one square km of solar collecting surface. And of course, even in a nuclear fission plant, the residual heat from the leftover radiation is insignificant compared to what went out the generators. Radiation is nasty stuff, and it can cause lots of problems, but it doesn't contribute to global warming.