If you have not replaced t-stat in awhile, I recommend for general maintenance at least. I recommend buying a mercruiser repair for look up and techniques. Mercruiser Stern Drive Repair Manual 2001-2013 | Seloc 3208
This is something that can be fairly easy to tested and best done by 2 people if you are a novice. I would think someone with decent mechanical experience can test out and repair within a safe environment.
The engine can be raw cooled or a closed system (coolant). I had found searching for "mercruiser 5.7 water flow diagram" that brings up a lot of imagines which you should be able to match.
Being that you have a 2100, I take it that you may have it trailered. That's an advantage for you vs me as my boat is a 3300 and is docked. Perhaps you have muffs for flushing the water? this can help in diagnosing the flow. If impeller, the flow then would be weak and should be inspected for wear and clogs. Replace if needed or if not down in some time.
On the 5.7 carb raw water cooled engine (like mine) the t-stat is on the top front of engine right behind the belt. There should be 4 hoses that go into the t-stat housing. you should be able to trace the flow up from back left of motor to the impeller (bottom left pulley) to the PS honeycomb cooler tube (at back) around right side then back to t-stat housing. The t-stat housing is channel internally for flow to engine water pump and both exhaust manifolds.
When I was looking a 5.7 over, I had taken off the main inlet water hose from t-stat to see the strength of the impeller flow while cranking motor. I had to make sure to stay clear of belts, pulleys, and have a bucket for water flow. Once I did see good flow, I clamped it back on and then went on to test t-stat.
I ran to temp again, used a infrared temperature gun to measure the temp of all hoses and various areas of engine, especially the temp sensor area, manifolds, risers, etc. I was able to see the rise in temp at sensor and housing. Flow then appeared blocked by t-stat. I'd say that if the temp sensor rises to above 165 then the flow should be seen by the t-stat opening (160 rated t-stat I believe) and then the two manifold hoses rise too. The temp gauge / sensor should have fallen. I'd tried tapping lightly on t-stat housing to see if it opened but it had not. I replaced t-stat.
Replacing the t-stat and wanting to do a good job, it will take some time. the repair manual does give some good info. One is that the gasket does have a metal grommet to provide grounding for temp sensor alarm therefore no gasket sealant should be used. I vacuumed out the bolt wells and dried everything out. I brushed the t-stat inlets and painted as needed. Ran back to temp and watch good rise and fall of temp gauge.
these two are not the complete set of items which can cause on overheat, but usually are the two that many can check out on their own. If you are up to tackle some jobs and learn more about the engine, the repair manual is a great way to go.