To my knowledge, the heat/heater core has nothing to do with the engine warming up. Having little or no heat is a different problem. How long does it take for it to reach operating temperature? Once it reaches operating temperature, does it fluctuate with driving? Sometimes it might take longer to warm up than other days depending on how cold it is outside. If the car's been warming up for a while (~15-20 mins) and no change in temp or very little then most likely it's your thermostat. It's a cheap fix and easy to install.