I'm not sure about it but I don't think it would be wise to drive around without a thermostat. You should check it by putting it in boiling water and see if it opens, it might be bad I think it opens at 160deg? you'll have to check on that.. You should also "burp" your coolant, that alone could be the problem even if your thermostat is fine. If there is air pockets in your coolant it will cause you to overheat and have erratic idle.