Sounds electrical. With no click, no sound, nothing, that would signal much more of an electrical issue than a fuel/engine issue. If I would be able to guess something seems to be shorting when the engine gets hot. I would give it a serious one over to see if something is shorting out somewhere. Look especially on manifold exhaust.
Also check all the spark plug wires for shorts.
Must it be 15 minutes always or is that just what you waited? Like would you try and try again in that 15 minutes?
If it does it again, quickly unhook the negative battery cable and put it back on and see if it starts faster than in 15 mins.
Also do remember your emergency brake as the problem sounds ghosty and not frequent.
