Yes, and engine can run too cool. Engines are designed to run at a certain temp, allowing for an expansion of pistons, rings, and such. Running an engine for extended periods at a significantly cooler temperature than the design specs will cause rapid cylinder wear. Back in high school, I owned an 87 Escort GT. Fun little car, problem was that the thermostat was bad and so the engine never warmed up. This was before I knew anything about cars, and I thought it would be an expensive fix. I drove it that way for a couple years. Eventually, the cylinders were so worn that the engine would not fire using the starter. The starter did not turn the engine fast enough to prevent the leaky cylinders from losing all their compression before they hit top dead center. I could get it started if I push started it, thus turning the engine over faster than the starter would. This way the cylinders did not have time to lose compression before they hit TDC. By that point, I could only get it to hold 60 MPH max.... lol
