300 ce 1989 starting problems

I have had this car now for around six years and have had to live with an erratic idling problem which appears without fail when the car is approaching around 80-90 degrees on the water temperature gauge. The garages that have been servicing the vehicle have never been able to find the problem.Lately I have not used the vehicle for a couple of months and had to recharge the battery as a result. I left it on charge for a couple of hour and then decided to take it for a run. As it approached the above temperature the engine began to get lumpy and hesitant on acceleration and misfiring until finally it gave up and died.Attempts to restart failed and in addition the battery went flat again. I called out a tow truck who delivered us home. I then recharged the battery overnight and in the morning the car started up without a problem. It reaches this point of warm up gets lumpy etc and dies out and efforts to restart even produce popping in the airfilter and prove useless until the temperature of the engine goes down.

I am hopeful that rectification of the the starting problem will also rectify the erratic idling I have endured for many years.

Please can somebody point me in the right direction.