why dose my 01 ls run hot only when ac is on

the heat of the evaporator has to go somewhere...unfortunately that somewhere is right in front of your engine coolant radiator...the transmission oil cooler is in that as well...so engine broils...there can be a thing or two that we can do....a NEW thermostat should be around twenty bucks....drain the coolant into old milk jugs and/or a five gallon bucket...take it to the autoparts store for recycling...get a gallon of Dexcool 50/50 or your preferred anti-freeze...flush the radiator (we used to use a garden hose at the shop, but that's a no-no (environmental wise) but if you can capture the fluid into a five gallon bucket and take that for recycling as well...the radiator flush would help...you could simply use the A/C to just take the edge off too---open the windows if at 30 mph or so~

Be sure to check the operation of your electric cooling fan. Easy to do: Open the hood,Start the engine, turn on the AC, look and listen for fan operation. Check that the Radiator and condenser aren't full of bugs ore even a plastic bag.

U need a new accuator on ur fan pump or air in cooling system

Tracy 01 have hydraulic fans not electric unless someone up graded them with after market