This vehicle is overheating. The temperature would climb slowly so the first logical thing to replace is the thermostat. A thermostat is not very expensive and is much easier to change than a water pump. They can be tested by boiling water and seeing if it opens. Due to the low effort and price its normally easier to just replace it. This vehicle is a GMC sonoma/ chevy s 10 with a 4.3 liter v6. Changing a thermostat is almost the same on any vehicle though, so dont be too concerned about what vehicle it is.
Here is the radiator hose that runs to the thermostat housing. The clamp can be removed by squeezing the clamp together where its v is. It will take a pliers or vise grips to squeeze the hose clamp, then slide it up the hose. It will no longer be holding the hose and you can twist and pull the hose off. You can see the two bolts that will need to be removed to remove the thermostat housing.
Another thing to do to make this job easier is to remove the air cleaner. Just undue the two cover screws and the air intake snorkel clamp and you now have plenty of room to acess the thermostat housing.
Here is the housing removed on the right side with the hose off and the thermostat still seated in the engine on the left side. Remember which way it is sitting in the engine so that you dont install it upside down in the engine. Thermostats need to be put in only in one direction and won’t work if put in upside down.
Here is a picture of the old and new thermostat. Some thermostats use a paper gasket between the housinh and the engine. Others as this one use a nice rubber seal around the outside. Its shown half removed on the left and correctly installed on the new one on the right.
Before reinstalling the thermostat always clean the housing and the engine mating surfaces. Brake cleaner and a razor blade can be used to clean the surfaces carefully, as to not damage the surfaces. If the housing uses a paper gasket you will want to coat both sides with silicon or rtv before tightening it back together. The rest can be done reverse of how it was dissasembled. Just make sure the thermostat is put back in the correct way. Refill the coolant and run the engine while watching the temperature closely. You may need to let it cool off and refill it again. Sometimes air pockets occur and require filling it more than once. If it still overheats then you may have a water pump problem.