I've started to have intermittent spiking of engine temperature, it generally happens when I'm moving slow or in traffic.

So I've learned that when the engine temp gets hot (as indicated by temp guage on instrument cluster), I turn the temp on the climate control to high and turn on the fan to relieve the engine of some heat. But today, when the temperature spike and I put the temperature over to hot, and blasted the fan the air was COLD! In addition to this, the temperature didn't go down either. I prayed the car wouldn't overheat and eventually hot air came through the vents and the temp came down but this happened a couple other times during my drive home from work. Is this an indication that the water pump is on its way out????