"Car heats up faster than normal" as you stated. If you compare it with your old thermostat, the old one may be slow. My 300SD gets to 80 deg from 10 deg by going about 10 blocks at night (with about 45 second warm up). With my old thermostat, my car was running at 80 deg all the time. I put in a new thermostat lately and the normal operating temperature is now 90 deg. My mileage seems to be 26 mpg now instead of 24 mpg in the past. It is obvious that my new thermostat rated at 80 deg is working at 90 deg. Maybe, you new thermostat is a little out of specification.

David