I watched an airstart in a Bell 407 during my days at Transport Canada - it will restart below 10,000 feet. Didn't seem too different than the normal ground start.
Having started at nearly 20,000' and tried twice with no start at high altitude will give you an idea of some of the issues.
That's why auto-relight should be standard for turbines.
Should be armed automatically anytime there is pressure in the transmission and the throttle is open.
Not sure what I'd do for a piston engine machine - the main problem is that unlike a FW airplane, there is no propeller to keep the engine turning over.