Black body radiation was my thought as well. It may not be the average including the inner layers, but it’s the average at the crust. About -1°F according to Wikipedia.
To add to this, is probably hard because the composition of the interior of the earth is a lot of guesswork. We can only directly observe how much heat is coming out of it.
I don’t know how easy it would be to migrate to your own local machine, but what you’re describing sounds like Desktop-as-a-Service. All of the major cloud providers offer this in some form.