Nonetheless getting rid of heat (by radiation) is possible, otherwise people would be roasted inside the ISS.
I'm sure all of these companies are advertising "ChatGPT in Space!" because that's what will generate hype and money, but what they'll actually be planning is very small edge data centers whose job is to reduce latency.
Whether that makes financial sense, I have no idea. But I am sure it's at least physically possible for a small enough data center.
That’s like saying „if you’re thirsty on a ship, getting thrown into the sea is actually really nice because you will be around a lot of water.“.
Physically, you could do it, but it won’t be simpler or cheaper than on earth. Except for constant solar availability, there are only downsides with this.