Engine problem or normal procedure?

I have a 85 Z non turbo. Just a quick question, when I start it up and drive it for about 3 miles at 60mph the rpms are up at 3 grand, then After those 3 miles it kicked down to 2 grand(normal running rpms) Is this what the engines are suppousted to do to get warm or is my Z just a werid pos like I always thought it was. Also the over drive button doesnt work for those 3 or so miles, only when the trany gets hot it works.

Thanks
AB

Sounds weird to me.... be sure to warm your car in the morning.