Just a slight correction. ABC/ABN engines pick up compression when they cool off, and have lower compression when hot. Ringed engines are the reverse, the ring expands as it heats, so a ringed engine will have less compression when cold and should have noticeably more compression right after running.

I agree with the rest of the above. Run the engine rich.

Ringed engines sometimes take a while to break in, and my experience with ST engines (limited to working on other guys engines) tells me that they take longer to break in than some other brands. This isn't a bad thing, just something to keep in mind. My older ringed engines were the same way, it takes a while for the ring to fully seat.

You'll also notice that the idle and transition will be tricky when the engine is new, and it's not at all uncommon to have the mixture changing on their own during break-in, especially the low speed.

If I had to guess, I'd say you low speed is a little lean right now. When you shut the engine down, it's going lean for just a moment, and therefore doesn't have fuel in it to re-start. If you are running the tank down or out, then the engine really is going leand right before shutdown. Once you mess with it for a few moments, it gets more of a prime in it, and starts up. So I think it's more the prime than the engine temp.

Try starting the engine up, running for just a few moments, just enough to get it up to running temp, then shut it down. Now prime it good, and see if it starts.