Overheating?

Hey guys this should be an easy one for someone more knowledgeable than me. My 2012 Escape limited Awd with the 2.5 is overheating, kind of. The radiator stays cold, my check engine light is on and the code I get off of it is p0128, which is coolant below temp after warm up. The only symptom my car has given me is that while idling my overflow tank will boil over even when my coolant gauge is showing completely cold. Im assuming it is either my thermostat or water pump. I dont know if there is anything else weird on this engine that could be causing it. Please I need an answer soon as I am moving cross country in 3 weeks and need to drive the car and would prefer to do the work myself but my budget is too tight to get both parts unless I need both.

Thanks yall

If it's boiling over and not getting hot I would check the radiator cap. For a few bucks it's a easy place to start.

I plan on getting a new radiator cap. What confuses me is why would my temp gauge show cold if its just the radiator cap. Im thinking its a combination of the radiator cap and the thermostat, I just dont want to start throwing money at this car if I can help it.

Is your heater blowing constant hot air when on if yes and radiator is hot then suspect thermostat. The thermostat addes pressure raising the boiling point of your coolant. If it's bad as the thermostat opens the coolant boils and out it goes.

Thats the issue, my heat works like usual but my radiator stays pretty cool to the touch. The only place that my coolant seems to be getting hot is inside the engine and the overflow tank. Im pretty sure my thermostat is bad just because of the error code Ive been getting but I still cant imagine that it would cause the other symptoms.

Feel the radiator hose if the thermostat opens the hose will get hot unless the radiator is plugged.