1993 Toyota Corolla DX-acceleration problem

I recently bought a '93 corolla DX, AT and lately I have been having a problem with the transmission during the cold starts, sometimes after the intial take off the engine just does not respond to the acclerator, I mean I accelrate but the car just does not go forward smoothly, instead it feels like I'm revving the car in neutral, the problem subsides after I stop the car for sometime and then go, its mostly during the cold starts. Can't figure out where the prolem is, is is the transmission? Or a tune up will solve it? Or is it connected to the speedometer malfunction problem I had earlier?
Wud be thankful if you could help me out