Barry, from my knowledge and first-hand experience with coolant circulating pumps of this type, a failure mode of loss of circulation is extremely unlikely. Water pump failures are usually related to the bearing or seal or both. If it's not leaking or making noise and the pulley isn't wobbling around, it is most probably circulating coolant. The exception to this is if a part of a vane on the pump breaks off, it can clog up the coolant passage. You might just take the pump off and have a look, to see if all of the pump vanes are there. (Make sure you have a fresh gasket on hand).
Thermostats are easy to check, in a pot of water on the stove and a thermometer. It will obvious open at the set temp if it's good.
As perhaps was mentioned, an IR thermometer, which can be had for under $20, is very handy for debugging cooling and heating issues.
On the other hand, air in the cooling system is often the culprit for the symptoms described. I've had this on a Universal M25 (Kubota D-850). The W-13 manual says to fill to the top of the filler neck, and the overflow tank to the bottom line, which I assume you did. On my M25, because of the circuitous water hose routing, I found I could purge the air by opening the net on the top of the thermostat housing and pumping coolant into the block drain petcock.
Do you have a water heater installed?