Raise the temperature of your radiator by 50 degrees and you double its emission capacity. Or put your radiator in the atmosphere and multiply its heat exchange capacity by a factor of a thousand.
It's not physically impossible. Of course not. It's been done thousands of times already. But it doesn't make any economic sense. It's like putting a McDonald's at the top of Everest. Is it possible? Of course. Is it worth the enormous difficulty and expense to put one there? Not even a little.
For thousands of years we never even looked to Mount Everest, then some bloke on the fiver said he’d give it a shot. Nowadays anyone with the cash and commitment can get the job done.
Same with datacenters in space, not today, but in 1000 years definitely, 100 surely, 10?
As for the economics, it makes about as much sense as running jet engines at full tilt to power them.