If it were me, and it's not, I would just go ahead and replace both the water pump and the thermostat. First of all, you'll have to drain the coolant anyway to do either so why not just do both together? We're talking about a combined $60 in parts (rockauto). Whenever I do a 2.3 to 2.5 engine swap I automatically replace these. That being said, they are much easier to replace with the engine out of the car. Sometimes the water pump takes a bit of force to extract from the engine block, which will be the most challenging part of the task.
Once all your new parts are in, park the car on an upward slope, or use jack stands to get the front up as high as you can safely. With the radiator cap off, run the car until the thermostat is open and continuously monitor the temp gauge as well as the coolant level. Run your heater. If you feel hot air from the heater it is a very good sign that you have purged air from the system, and that you pump is circulating water appropriately.
Please do not risk your engine for $60 in parts. That is unless you want to learn how to do the 2.5 swap, which will surely become a necessity if you keep overheating your engine.