My Ford Taurus heater takes forever to get warm - I replaced the thermostat?

Thermostat come in different temperature ratings - meaning the valve opens at a specific temperature.

Likely your new one is a higher temp (192?), thereby keeping the coolant from getting to the heater core until that higher temperature is achieved.

Not sure what the specific numbers are, but you might want to swap it again for something lower (180 degrees?).