Service battery charging system is on the display and then it flashed a/c shutting off due to engine overheating. Took out thermostat to open flow and same thing also took off pressure side of water hose and it is pumping water fine. The temp gauge does not move but it isn't low on water. Battery and alternator test fine. Service battery charging system has been showing for a while with no results on searching for source. Now this. Any help would be great please. I'm lost and can't afford a shop it's my mother's vehicle and it's needed for work. Please and thank you .

 

What year/make/model vehicle is this and which engine does it have? It's hard to give any advice without this information.