Suzuki 2 Strokes

Mark did you check the temp of the coolant with a thermometer after the gauge began to rise to the middle position? If its within spec id remove the cover on the cylinder head and perform a thermostat test next to see if its opening.
The fact you saw no fluid movement is a sign the systems flow is blocked somehow.
Report back on whats the status of the temp and thermostat first before moving on from there.

Yes you are correct,the temp sensor and thermostat are mounted inside the top radiator hose connection cover where it enters the cylinder head.
With a chequered history of many POs anything is possible on an old vehicle.

Very hot on one cylinder tends to suggest a problem in that one cylinder.

Before you panic though, I'd agree with Allan's approach to check the cooling system. In fact I'd probably pull the radiator and flush it out and then flush the water pipes and remove the thermostat and check it in a pan of hot water on the stove when SWMBO is not around.

Then I'd look for signs of air leakage on that pot. It could be anything from a cracked intake rubber, to bad crank seal behind the alternator. If that all looks OK, clean and check the points and check the timing.

In other words, give it a good service and fresh oil and fuel before worrying too much. A nice fresh set of plugs won't hurt and while they are out, check the compression across all three pots.

One run every year is also close to optimum for getting the carbs clogged with old fuel and laquer, so I'd pull them and clean them and the whole fuel system out.

Sound like a plan?

Here was a little prep list i had posted over at another thread for a 76 Buffalo:

Remove the fuel tank petcock and check the three filter screens.
Inspect the tanks innards and clean it out if necessary with some water based rust remover.
Remove the carb rack and clean them throughly and do the air jet mod if its not done already. (Not for your 72/73 model)
Check the float levels and adjust them to spec if necessary and get new bowl gaskets.
Check the six rubber boots on the intake and air cleaner sides of the carbs, if they are hard in any way, get new ones as air leaks will create havoc on you and the engine. Make sure the six metal clamps on them are in good condition
Perform a cylinder compression test and see what figures you get.
Get some new B8ES NGK spark plugs.
Check the points and condensers, if the points look acceptable clean them up, get at least three new condensers since you do not know the age of these items on the bike.
Adjust the points gaps and set the timing statically for now, make sure your battery is good and holding a charge.
Make sure the airfilter is clean and the sponge is freshly oiled. (not for the 72/73 model)
Change the tranmsission fluid.
Drain and refill the coolant if it looks suspect or just because you should.
Remove the premix oil tank and clean it, put in a good quality two stroke oil.
You can bleed the line to the oil pump once its been refilled.
Ok after this long will of things to do, you'll be close to ready for a test fire.

Id run through this list as well as what Richard has said about removing the rad and flushing it, plus checking the hoses etc for any surprises.
I hope the non flowing issue of water across the filler neck does not mean you have to go digging into the water pump cartridge as well, BUT lets take it one step at a time for now.

Fortunately that bike has normal VM carbs with reasonably large passageways, and not those pesky BS40 CV carbs with lots of tiny holes to clog.

If only one cyllinder gets very hot it might be related to the exhaust. On my T350 one cyllinder was hotter than the other and it turned out to be a wrong baffle pipe in the exhaust. So maybe you have one plugged exhaust?