Your point is well made. If all it took was heat, then climate change would probably be the best thing ever. More heat captured from the sun would give us more energy.
There were some people seriously proposing big convection tubes that'd bootstrap columns of hot air, then passively pull surface air into the upper atmosphere. I can't find a link, but those wouldn't get to low earth orbit, so not a "space" technology.
That'd have the same net effect as the giant heat sink (energy production from a heat engine, net negative flow of energy to the surface).
Wasn't there a city builder that'd let you build such a thing, where it would sometimes lose calibration and burn a swath of the city to the ground?