Basically... just pull harder! Once the housing is removed the only thing holding the t-stat i place is simple friction. In the case of your 4.7, it uses a rubber-like gasket that's possibly hardened and is certainly embedded.
Since you will be replacing the whole assembly, there's no reason to be gentle. Stick a pry bar in the upper bridge and lever the assembly out if needed. Just don't mar the sealing surface to avoid a leak once done.
Write back if you have any questions.
Good morning! The 4.7 hides its thermostat in a housing near the water pump. Remove the two 8mm hex bolts at the lower hose where the hose connects to the engine. The 'stat doesn't use a separate gasket in this case, but has a molded rubber outer seal. There may also be a notch molded into the seal to orient it to the housing correctly, so that the "jiggle valve", the automatic air bleed hole can do its job effectively.
Make sure the spring side of the thermostat faces the engine and bolt it back up. Very little cooling system bleeding is needed in most cases... the engine fills almost to 100% immediately, but check it again after it's reached operating temperature and cooled again.
The engine coolant temperature (ECT) sensor is located atop the engine, in front and just back of the water pump. It's a brass unit, using two wires. You need a 19mm deep socket, one with no step in it for removal. Craftsman makes this type of socket.
What kind of problem are you having?
Tough call. When the temp gauge rises gradually as you've seen, it normally indicates a true temperature from my experience. It might not boil out, but I have a feeling it really is getting hot.
Make sure your coolant level below the radiator cap is up to level for starters. Low coolant levels lead to uneven circulation and hot spots in the upper reaches of the engine, where the ECT lives.
Somewhere near half-scale the thermostat should open and flood the radiator with hot coolant. The crank-driven fan will turn the air passing through the radiator markedly hotter at that point, something that you should be able to feel. If the temp gauge passes half and you're not feeling heat in the upper radiator hose or heated air coming through the radiator, it may very well be the thermostat that's causing your problem.
A rough method of telling whether the engine is overheating is to spray water on the exposed metal in the upper end of the engine... the cylinder heads are handy for this. An engine running at a nominal 200 degrees will not boil this water off, no matter what the gauge says. You can use this "measuring stick" to trace water flow and heat from any point in the cooling system if it does get hot on you.