Other than buying new hardware, I have an old rig now, mine is from 2009.... a old single core AMD Sempron LE -1300 CPU, but what I did was upgrade the PSU from a 250w to 430w Thermaltake, that way it has more power, upgraded the RAM from 2 GB to 4 GB, (max my mobo supports), and put my older GeForce GT 220 GPU inside as well, until I can buy a new PC.
Now, if you can't buy new hardware, in game options can be tweaked to allow better performance. For one, turn down the resolution, say your running at 1600x900, well turn the game down to 1280x720 or somewhere lower than current, than turn down visual settings if game has down to medium/low.
I can run games that are for Dual core CPUs and whatnot, such as Dear Esther, Amnesia etc. on my single core, sure the GPU fan speeds up, but nothing too drastic, stays at 87 degrees Celsius under load, than cools off to 50-55 C idle, and the game runs fine. Some newer games might not run, at all, but most of the time, just lowering resolution, and low visual settings helps FPS in most games, you could also tweak the GPU settings in the NVidia control panel. Like select instead of best quality, lower the settings down to "Performance" and turn off AA and other GPU intense features.