It's all but impossible for a mechanic to find and fix a problem that doesn't exist when he's working on the vehicle. That's what makes transient problems so difficult to correct.

There are some things you can do to help trace this problem, and it involves spark and fuel. The next time it fails to start, stop trying to start it. Check for fuel rail pressure and then for spark.

I don't know where the pressure test port is on your particular fuel rail, but find it. At the least, learn where a fitting is that you can crack to check for the existence of pressure. You want to check and see if gasoline squirts out under pressure. You may want to test it right after it's running right a few times just to see what the gasoline squirts out like under proper pressure. You want to see if it's squirting out like that when it doesn't start.

Next is spark. You want to check for spark at the plugs, or at least one plug, when it doesn't start. You're looking to see if you don't have spark going to the plug(s) when it's refusing to start. If you use a lawnmower type spark tester, it's pretty easy to check.

Don't go "aha!" based on one test. Do it a few times, looking for a pattern. With that pattern, we on this board and your mechanic can continue going on locating exactly what is happening.

Heat soak has to do with things, particularly electrical things, get hot to the point they don't work right. Hall sensors inside electronic distributors for example. It can be quite a problem with components located around exhaust manifolds. Nissan had such a problem with heat soaking on some engines back in the 70/80's, they installed a little electric fan on a timer for some cars. Crude, but effective.