The exhaust temperature of the AC will be as low as is practically possible to remove a given amount of heat (assuming the AC is properly engineered). To extrac

The exhaust temperature of the AC will be as low as is practically possible to remove a given amount of heat (assuming the AC is properly engineered). To extract energy from this exhaust you have the problem to remove heat from the cold end of your stirling engine while maintaining a lower temperature than the exhaust, which will prove difficult, given the assumption. OTOH, if the exhaust of your AC is hotter than necessary (the unit wastes energy), then the best you could hope for is to recover some part of (depends on temperature differential) the wasted energy. Better get a better AC unit.