cold start, high rpm & surge

'87 Integra automatic. Cold start, engine revs immediately to 2400 rpm, then after 10 seconds or so, idle starts to surge from 2200-2400 every 3-4 seconds. Tapping the throttle has no effect (unlike my old '78 Accord). After a minute or two, rpm begins to slowly drop and surging decreases as engine warms, eventually getting below 2000 after about 3 minutes. Previous owner messed up the transmission by not waiting for rpms to drop before putting it in gear. Warm starts are normal. Thanks.

So let me see if I am understanding you right. When it is cold the engine surges like you described. But after you drive the car and the engine is warm, you can turn the car off and then start the engine back up and it runs normal?

Yes. So long as the engine is warm, everything is normal, including restarts.