Even though you do have less greenhouse gases to trap the heat, you will be pumping more of that heat into the atmosphere, seas and oceans, warming everything up.
You're removing one aspect of climate change but not all aspects of it, still affecting the climate and ecosystems.
Also, for example, we still can't fly passenger and cargo planes with electricity for now, so you won't be able to remove all greenhouse gases, yet.
Look at the data [0]. Yes, energy production and heating is the biggest contributor, and even if you manage to remove it completely with the transportation sector via electrification, half of the emissions are still there.
The amount of heat pumped out by humans this way is so miniscule compared to natural flows that this is a complete non-issue on a global scale, and will be for a very long time.
I work at a datacenter. We provide compute resources to researchers, and while our datacenter is not small or low energy, one of our systems have Green500 certification and we try to do things as efficient as possible.
When I look at our racks, some of them are DLC BTW, and imagine each of them can pack a MW system now, I shudder. Not because of us, but what AI datacenters gonna do with that energy density and how much heat will these systems put out.