Now, if you wanted to build a nuclear power plant in space and beam its power, then heat dissipation would be a big problem.
i think this depends in part on how high a temperature you can tolerate; at 20° the stefan–boltzmann emissivity is only 420 watts per square meter for an ideal black body, a third of the above-the-atmosphere solar irradiance. the blackbody equilibrium stefan-boltzmann temperature for 1300 watts per square meter is 116°, which is a bit toasty for efficient solar panels; even at half that (if you're emitting infrared from the back of the pv array as well as the front) you're at 54°. and if you want to move your power plant closer to the sun to harvest that sweet, sweet radiation, the temperature goes up further
so plausibly some heatpipes painted black sticking far out the backside would be helpful
rectenna arrays might have been a reasonable idea when solar panels were expensive. they're still reasonable if you're willing to use a microwave beam that's concentrated enough to be a devastating weapon of war. sunlight is 1000 watts per square meter, and that's already enough to heat up a tin roof or the interior of a car to temperatures that will burn or kill. if you boost that by a factor of 10 or 100, you could get a higher-density "power plant" on the ground that's cheaper than the equivalent solar farm
but you still have to build the solar farm, you just build it in space. right now that's much more expensive, and, as jacquesm points out, rejecting waste heat in space is more difficult. there are a few possible ways that building it in space could be better:
1. if robots are mining asteroids for minerals, they can build solar panels in space that don't have to survive earth weather, or for that matter launch or reentry. plausibly they could be under a micron thick, thus using thousands of times less material than earth solar panels. conceivably you could even do this with terrestrial factories if you have cheap enough and gentle enough launch, which you don't, but maybe with bfr you will
2. if barbarians are mobbing your castle with pitchforks and torches, banning borax and methyl ethyl ketone, coercing you into swearing loyalty oaths, or threatening to put your family in ovens because of your ethnicity, you might prefer to have your solar panels somewhere they can't reach
3. to make the transition from a kardashev type 1 civilization to a kardashev type 2 civilization, obviously covering the entire earth with solar panels is insufficient, so you have to put them somewhere else
4. you can put the solar panels much closer to the sun than the earth is, so they produce much more power per unit area
obviously none of these are relevant right now, but sooner or later they will be