A perfect vacuum might have no temperature, but space is not a perfect vacuum, and has a well-defined temperature. More insight would be found in thinking about what temperature precisely means, and the difference between it and heat capacity.
To illustrate the point with a concrete example. You can heat something with the thermal transfer rate of aerogel to an absurdly high temperature and it will still be safe to pick up with your bare hand. Physics says it has a temperature but our intuition says something is wrong with the physics.
Yes I'm making that argument. Because it's true. The temperature of what particles do exist, 500km above the earth, is more likely to be in the thousands of degrees farenheit than below zero farenheit.
The discussion being had, if you read comments above your original, is that it's widely thought that "space is cold" and therefore it's good for cooling.
You're right that heat capacity means that the temperature of space is not relevant to its ability to cool a datacenter. You're wrong that making that argument is a good way to get people to actually change their mind.
Instead, attack the idea at its foundation. Space is not cold, not in the places where the data centers would be. It's much easier to get someone to understand "the temperature at 500km where the auroras are is very hot" than "blah blah heat capacity".
Now you see the point!