Well, first off, is this a tiller or remote control model? Not sure but a D1 is supposed to be a 2001. No matter, they're all the same anyway.
I will say that, in my experience, the SE auto thermo valves rarely fail. But I have had to replace a couple of them over the years.
The SE valve is defaulted to "enrich" when the engine is cold. So, even if the heater coil were bad, the engine should still start normally and then, after about 1 1/2 minutes of warm up, it would begin running too rich. The longer it runs in the enrich mode the worse it will perform and, ultimately, it would likely stall as a result. Not the symptoms you describe.
But another way that the valve might fail is to get stuck in the extended or lean position. This can happen if there is no problem at all with the heating element and would cause hard starting when cold but normal operation and easy starting after the engine warms. Closer to what you describe.
The resistance values William01 gave you are correct if you want to check the coil's resistance. But you can also remove the valve and test it by applying 12vdc and watching it's movement. You can do that without removing the carb. Based on the symptoms it's probably something you should check.
But something that you wrote has me scratching my head. You said that it floods and you see gas coming out of the carb drain hose. The carb shouldn't flood with the SE valve stuck in the lean position.
Also, the only way gas could come out of the carb drain would be if the drain screw is loose.
I could see gas running down the outside of the drain hose if the carb were flooding but not out of it. As a result I would have you check the drain screw and ensure that it is snug and that the drain isn't leaking.
With the carb flooding it may have a different problem than the SE valve.
QUESTION:Are you opening the throttle several times when you are trying to start it?
If so, that could be shooting gas into the intake because you are activating the accelerator pump. That might be flooding the engine and making it harder to start because it's quite a load of unatomized fuel per stroke and a cold engine can't handle it. That still doesn't explain gas coming out of the carb and down the drain hose.
QUESTION: Is the little black bellows on the side of the carb in good shape. No holes or tears?
Anyway, let me know if you want to remove the valve and test it. I will look up the correct wire to apply the positive to since I can't remember at the moment.
