To the best of my knowledge to measure the temperature of the exhaust
gases as they enter the rubber exhaust hose point the IR meter at the top part of the hose within about 6 inches of the attachment point where the hose is clamped to the engine
exhaust exhaust water
injector. This is the most vulnerable area of the hose to being "cooked." Any reading near or over 200°F (the hose's stated max temp rating) is a problem that needs attention.
Finding out why the temp is so high is important as you may have a clogged or corroded injection nozzle which is bound to happen eventually as they are normally made of iron. Likewise as discussed earlier, a damaged or broken R.W. pump impeller, etc. can restrict water
If everything is "normal" - that is, no restrictions or other problems, it is possible to switch out the portion of the exhaust hose closest to the engine
and replace it with "blue silicone" type exhaust hose which has a max rating of 350°F. However, the cost of silicon hose is significantly more than the usual black rubber exhaust hose.
As to the engine cooling
system thermostat - getting readings as the engine heats up to its normal operating temperature should reveal what is happening. Generally, but not always, the thermostat is located inside a globe shaped or elbow
shaped casting above the engine's fresh water pump. Point the IR meter at the casting should reveal the temperature that the coolant
flowing inside. You would expect a steady climb in the temperature and then a stabilization somewhere around 190°F for a diesel
engine. That is going to depend upon whether the coolant
passing through the thermostat housing is coming out of the engine block galleries or somewhere else.
As to where to purchase
a digital IR thermometer - I seriously doubt Home Depot would have them. It is more of an automotive or "shop" tool. So places like Harbor Freight or just an internet
search would be the most productive. They are probably even available on Ebay.