P0125 code?

Pluged in my code reader, to check why check engine light was on, it gave a code p0125, and code says, insufficient coolant temperature for closed loop fuel control. Temp gauge reads a little over half way up on gauge, checked engine temp and it seems to be fine, heater puts out good heat. Could it be my engine coolant temp sensor, giving the computer a false reading? If so should I replace it?Your help would be aprechated.