Overheating

Hello, I have a 2001 mustang gt completely stock. I drove to panera the other day and the car was fine while driving, i got it up to temperature and after idling for a minute or it began to creep towards hot. The fan was running and it didn't seem to help. I shut the car off and let it cool, I made it home by stopping when it was getting a little too warm. I suspect several things and I was just looking for some other advice as to what it might be. It hadn't given me an issue like this before. 1. The High Speed Fan Controller thing in the radiator, I read that they go bad. 2. Bad thermostat, which I will be testing soon. 3. Bad fan motor, it would spin but maybe not fast enough. 4. Any advice would be very much appreciated. I have considered getting a new water pump as well, as a maintenance item.

So here's whats been going on. I am planning on making a full write up once I am certain my new edge is fixed. Yes, the thermostat no works. It stuck closed which was causing me my issue. Additionally, my radiator cap didn't hold the pressure and now releases coolant when the car warms up. Neither did the two brand new caps I purchased, so I still need a cap. As maintenance for my cooling system, because of how many times I have drained and refilled it lately, I want to just revamp the cooling system. I will be installing a new radiator, new water pump, and the proper type of gold motorcraft concentrate mixed with distilled water. Them I'll buy another radiator cap, test it at my work, then I should be good to rip around town again.