YM2000 was late 70's. My YM240 (see my sig photo, below) is the US version of it.
You could disconnect the radiator and use a garden hose to verify that what goes in the top, isn't blocked from coming out the bottom.
If you have hosed off the radiator exterior and its reasonably clean, and the tractor overheats while you see a swirl in the top tank, those are the classic symptoms of a blown head gasket. Since this can let water into the cylinders, it is imperative to crank with the compression release used, to blow any water out of the cylinders when starting, until the actual cause is found. (Water is incompressible, it causes expensive damage).
If the radiator looks ok there's not much else it can be. (The swirl eliminates a bad water pump. (and the YM1700 smaller twin to these didn't even have one.) When the cooling system is up to spec both models will run at full load all day and stay cool.
Replacing the head gasket is no big deal on this simple two-cylinder. I have the original Yanmar flat-rate manual and it says bill the customer 2.4 hours labor to R/R the head and gasket. Hoyetractor has the head gasket.
http://www.hoyetractor.com/mm5/merchant.mvc?Screen=PROD&Product_Code=2000-HEADGASKET
[What would that project cost on a modern utility tractor, guys?

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And Welcome, Dean! There are still a few of us owners of these elderly Yanmars on this board. In fact I just bought a third one, another early 80's YM186D, this one with loader and power steering. Otherwise it looks like the YM186D (red) in my sig photo.