Heater is blowing cold air, check engine, ETC light, and check gauges light are all on.

Problem seems to cycle - driving along, suddenly the check engine light comes on along with the electronic throttle control warning light, as the temp gauge drops to zero - which triggers the Check Gauges warning light to come on. Drive more, stop a few times, ETC light goes off, temp gauge starts working again. Check engine light stays on for a while, then goes off. Some miles/hours later, cycle repeats. No indication of trouble in engine behavior, sound, except for the heater is blowing cold air with intermittent warm air blowing for a short period of time. (I know this sounds familiar, and it is compliments of Mitchkeos (December 31, 2013), with the exception of the heater blowing cold air). AutoZone ran the computer on it and it showed “Engine light on- found faults for cooling system performance”. My questions are: Are these problems related? Will replacement of the thermostat fix the issues? Or do I need to replace the temp sensor sending unit as in the case of Mitchkeos?