I remember the BMW M3, I believe this is back in E36 period, was tuned so that until the engine reached its optimum operating temperature, the engine would not rev past 3000 rpms to prevent impatient and/or overzealous owners from causing damage to the engine.
Considering how problematic our cars can be without doing anything wrong, I'd definitely say make sure you let the car get warm before you play. Keeping the RPMs above 3,000 (but under 4,000) will certainly get you to that point within 5-10 minutes depending on how much of that time is spent in motion.