My first thought is that you have a severely slipping transmission, and that continuing to drive it like this will only increase the repair bill for the transmission. I am basing that opinion on the fact that the car was apparently going only 20 mph while the engine was turning over at 3,000 RPMs. Normally, at 3,000 RPMs, your car would probably be traveling at something over 70 mph. This type of disparity almost always indicates a badly slipping transmission--if you have an automatic trans. If you have a manual shift, then your clutch is worn out.
(Since your engine's idle speed is probably something in the area of 600 RPMs, clearly the engine could not be running at 30 RPMs, as you stated.)
It is not unusual for some types of transmission problems to be less severe when the engine and transmission warm up fully, but that improvement does not mean that the trans problem has disappeared. More than likely, you will experience the same thing when you start the car tomorrow. However, rather than driving it, I would suggest that you have the car towed to an independent transmission shop for diagnosis. DO NOT go to AAMCO, Lee Myles, Cottman, Mr. Transmission, or any other chain unless you want to be told that you need a new transmission--whether you really do or not.
Before having the car towed to a trans shop, you might want to check the transmission fluid in the AM, and refill if necessary with the correct spec fluid (some type of Dexron, and your Owner's Manual will tell you which version is correct), but if the transmission is low on fluid, it still needs professional attention as trans fluid does not evaporate, and a low fluid level indicates a leak that needs to be repaired.
Just on the possibility that other forces are at work here, it would be helpful if you posted the car's maintenance and repair record over the past 3 years, but I am still fairly sure that your transmission is the problem here.
Please post back with the outcome of this situation.