No thermostat on a daily driver = bad idea. It will stay cool for a while, and take a long time to heat up.. but when it does heat up, it won't cool down.. your car will just overheat. This is because there is no thermostat to close and hold water in the block/radiator.. it just constantly flows.. so the water doesn't stay in your radiator long enough to transfer out the heat.. it just stays hot.
Put a brand new 160 or 180 in, and make sure it's installed correctly. If you're still overheating, investigate problems elsewhere. Fan functioning properly/spinning in proper direction (if the wires get crossed and your fan starts blowing on the radiator instead of on your engine, you will have overheating problems. The air will blow in from the front, then your fan will blow it right back out, and it will 'stall' the air on your radiator, instead of cycling it through), water pump going south, junk radiator, etc.