The heat problem has demonstrable solutions that people who are physics challenged can't seem to get themselves to accept.
Which would be relevant if solar panels or land were scarce and expensive. Neither are. It's easier and cheaper to put 4-10X the number of panels on land.
The critics of space data centers seem to be focused on the immediate instant and downplaying any potential tech improvements.
Only if you ignore the cost of getting in there
My searches aren't turning anything up, would you mind sharing what you know about solutions to the heat problem or point me towards a resource if can learn from?
https://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law
https://en.wikipedia.org/wiki/Radiative_cooling
You don't in fact have viable solutions to this problem when orbital launch prices are above like 100USD per ton, probably needs to be closer to 20USD per ton.
Go on then, what are they? Demonstrable, you said. Show us some demonstrations please.
If datacenters in space become a thing, you'll hear your neighbor talking about how rockets poison the air.
The total atmospheric pollution from rockets, even at that scale, will be small compared the total from terrestrial sources but unfortunately atmospheric pollution works like real estate: location matters.
Orbital rockets deposit stuff into the upper stratosphere which is about the worst place you can put. Things there have effects massively disproportionate to the same amount of the same things emitted into the lower atmosphere by terrestrial sources. Some have up to 500x the effect when emitted in the upper stratosphere than when emitted by airplanes or on the ground.
It's been OK so far because in the entire history of rockets there have only been about 7500 orbital launches (which are what matter for the upper stratosphere--see below). With a million space data centers which are expected to each have a useful life of 5 years there would have to be about 2000 Starship launches (@100 data centers per launch) per year just for replacing the ones that have reached EOL. That's after the 10000 launches for initial deployment.
Worse, satellites damage the upper stratosphere on reentry. With a million space data centers that's 200k reentries per year. The cumulative number of reentries so far is around 10k satellites and spent rocket bodies, and around 25k if we count smaller things that we can track like debris.
There have been tens of thousands of suborbital launches that have reached the upper stratosphere but most of them have been sounding rockets which are small enough that the cumulative pollution from all of them is less than a year's worth of current orbital launches. On top of that most of the sounding rockets were for weather monitoring and have been replaced by balloons. Current sounding rocket use is negligible. There have also been ballistic missiles but by the time those are in the upper stratosphere they are ballistic and don't pollute much. Hence it is only orbital launches we have to worry about.
If they were talking about putting them on the moon I'd get it; use the moon itself as a giant heat sink. Latency isn't ideal but for applications where that's not a problem (like AI; 3s round trip isn't meaningful in the context of a chat session) then why not.
I'd also wonder if the folks who don't want to live within 3 miles of a data center are OK with the data center flying over their head
They stand in the way of a nearly limitless number of positive outcomes from this technology and directly have blood on their hands that they wipe away with thought terminating cliches like "precautionary principle"
The obvious alternative explanation is that people are very worried about the externalities of a project as massive as putting data centers in space.