2007 Aveo slow to heat up or won't heat up at all

Hi all, I'm in need of some help please. I have a 07 Aveo 5 spd manual transmission that has a heating issue, when I have been driving the car and the engine is hot or gauge at normal and I stop at the store or to get gas then start engine back up it begins to cool down rapidly and sometimes it will get hot again (when I say hot I mean a normal gauge reading) and sometimes it just stays cold with no warm air coming out of the vents, the thermostat was just replaced as of this post and now it takes forever for the gauge to go to normal..... There were no signs of contamination in the coolant in fact it was very clean for 160k miles and being DexCool. Could this be a water pump?

This has been something that just happened it was not a gradual problem.