Hey Scotty! I got a problem i bought a 2014 Cruze And When i started driving the temp started to rise uncontrollably then it gave me a message saying the AC Was off due to a high engine temp.. And then spiked way up after hitting the brake, And then when i stopped the vehicle, It went back to the normal range (Usually the middle) What could be the issue... Be Mindful i just bought this car Today.

Also to add, They also drove the vehicle 600 Miles additionally and this issue never happened

I also wanted to also add into this, The Car was still cold and blowing cold air through the cabin when the heat was turned all the way up.

Plugged heater core

I would change the thermotat out, that new I doubt the heater core could be plugged already.