Wow I have the exact same issue on a 2010 CRDI with 225,000 on the clock.
I started a topic on it ages ago but I never had any responses with any idea's or suggestions so I though it was very rare , good to hear I'm not the only one.
Still have no idea why , a mechanic friend suggested maybe a leaky injector and when it's warm the viscosity of the diesel is less so more leaks into the cylinder before startup , does this make any sense to anyone ?
It starts perfectly every time when it's cold , almost instantly , so definitely the glow plugs are ok.
But now we are getting into the warmer months , it has started doing it again , it will run real rough when it does this delayed start and continue for about a minute or two before it clears itself while idling (I always warm the car for a few minutes before driving)
So sometimes it will take me two crank cycles , I never sit there just continuously cranking the engine , I only do it for about 5 - 10 seconds max then stop and go again , on the second attempt it will always start like normal , it's only ever on the first attempt to start when warm it will do this.
Also when this happens there will be a lot of unburnt diesel coming out from the exhaust but never any sign of this when it's cold air temp.
It's almost guaranteed it will do it when the temps are higher eg Air temp < 15c no sign of this issue and starts first time every time , Air temp > 15 getting closer to 18c - 20c definitely will do this delayed start.
This issue has pretty much been there since I purchased the car at 80,000kms , it hasn't got any worse or any better and only happens when it's warm weather.
Any tip or suggestions would be greatly appreciated.