3500 RPM Hesitation

[FC Zach]

Im helping a friend with his 88 NA, factory car except for the air pump being routed straight to the cat (which is another question I have). His car was hesitating at 3500 RPM and idling low and rough. It drives ok untill then, then it's like the car just falls on its face. I broused around looking for obvious signs of a problem and found one problem, the vac line going from the pressure sensor (passenger side shock tower) to the LIM was disconnected. I pluged it back up and we went for a test drive. The car idled better but the hesitation was still present. We stopped by Advance to get directions to do a diagnostic check but the Haynes manual was for 89 and on, so I disconnected the battery, waited a min, and went back to the house. Nothing was reset and the problem was still there. Later this evening while I was at work he called and let me know that the hesitation doesnt occur when the engine is cold. You guys have any ideas? Anyone had a similar problem? And about the air pump, is it bad to have it connected straight to the cat constantly. I keep hearing both sides of the story. I dont see any problem with it but want some more oppinions.