I've had the same issue twice now - get in the car, turn radio on, and only the front tweeters and rear work, door speakers are not producing any sound.
Last time it took 15 mins, today it took 30 mins of driving and then the drivers speaker crackled for about 10 seconds and gradually came to life. Then the passenger door speaker did the same thing a few minutes later.
All a bit wierd really - the amp feeds an inline crossover (in the doors) which then feeds the tweeter/mid. I initially thought it was the amp as the last time it was only the drivers mid that was off, but today it was both speakers. Today was also the coldest day I've known, -8c on the dash gauge.
Could the door speakers be damp (likely), which is frozen stopping them from moving, which then thaws out after a bit of driving?