Engine running very hot but plenty of coolant - is it related to recent a/c work? on 1997 Mercury Villager

Recently had the a/c compressor replaced in my 97 villager and all seemed to be well, however, I noticed that at stop lights, air seemed less cool than when the car was running. At the green light, when I first accelerated, warm air blew in even though a/c is turned on. I also noticed that the engine temp. gauge is running almost to overheating point. The engine seems to be "cycling" loudly as though it's trying to turn something on but can't. I checked the coolant level and it's actually above the Max line - done by the garage I suspect. Could overheating prob. be related to the recent a/c work done?

Asked by for the 1997 Mercury Villager
when u turn your ac on do the radiator cooling fans come on or if they are already on do they speed up after a few seconds when condensor heats up the cooling fans should run at a low speed to cool condensor when engine gets to running temp opproxamatly222 degrese fan should cycle between low speed and high speed.this is a very proper answer would like if u would email the problem to me once fixed thank u
1 more answer
tryin to find an answer to a very similar problem. replaced compressor,dryer,cooling fan and runs fine now but when air is off and fan cuts on the temp gauge jumps from normal to 1st hot line...then cools back down...wondering if air in system.