An old gaming PC is not inherently much worse than any other system as a simple server. If you want to save money, you can just keep using it, but it might be worth reducing the power consumption.
You could start by removing or disabling unnecessary components:
- remove the GPU if it's not in use
- go into your BIOS and disable anything that is not in use, such as PCI Express slots and USB slots
This can significantly reduce idle power consumption.
As a next step, you could install Linux, which may reduce idle power even more by using fewer system resources.
But all in all, there is no better solution to your heat problem than to move the server to another room. Even my Raspberry Pi and router together produce a noticeable heat in my room.