Even the ISS has sizable radiators. The Shuttle had deployable radiators in the form of the bay doors if my memory serves me correctly.
Oddly enough the otherwise dumb Avatar films are among the only ones to show starships with something approaching proper radiators.
There’s no air resistance in space so radiators don’t impact your flight characteristics.
> Next [after loading the computers with on-orbit software] we opened the payload bay doors. The inside of those doors contained radiators used to dump the heat generated by our electronics into space. If they failed to open, we’d have only a couple hours to get Discovery back on Earth before she fried her brains. But both doors swung open as planned, another milestone passed.
I imagine it's the same reason James Cameron is a world expert on submersibles - the guy picks individual topics in his movies to really get right.
I'm pretty sure it was that series that also described https://en.wikipedia.org/wiki/Liquid_droplet_radiator , with the side effects of different ships having very distinct heat patterns because of their radiator patterns. And that if a ship ever had to make a turn while they were active, big glowing arcs of slowly-cooling droplets would be flung out into space and leave a kind of heat plume.