The first thing that comes to mind is to check to make sure that the electric cooling fan for teh radiator is running whenever the AC is turned on; if not, the car will overheat very quickly.
If teh fan is operating, then the likely scenario is that teh car's cooling system is not operating as efficiently as it should. If a cooling system is doing a marginal job of keeping teh engine cool, then the added load of the AC heat could be enough to push it past it's capacity.
Things that could affect cooling system capacity would include:
(1) bugs, dirt, leaves, or other debris restricting airflow through the condenser and radiator. Especially check in the space between the rad and condenser; leaves often end up in this space for some reason.
(2) Internally restricted coolant flow through the radiator core, due to deposits from not changing the coolant on schedule for maintenance. This is very common.
(3) possible failing water pump, not circulating coolant as designed. This is more common on some models than others.
I hope this is helpful...