I used Normal a lot over the last months and just recently and each time I start up the car in Normal (after leaving it in Normal) the responsiveness is just Normal, certainly not as lively as Sport (once the switching out and in is done)
There were times when I was driving in Sport (started in Sport) and when switching to Normal the car felt livelier - So for me starting in any Mode I don't seem to get the best out of that particular Mode without switching.... Although I only really use Sport, Normal & Individual (set to Sport in most)
With that said and Normal mode seemingly more responsive at times I'm still not convinced the engine is defaulting to Normal. So regardless of the car being warm or cold how can Normal mode give at least 2 different feels in responsiveness. I remember reading some reviews that the GTD Normal mode was just as good as Sport if not just slightly behind it, but in my opinion its quite far behind Sport until you perform the Mode switch.