There is no doubt that with more demand placed upon the engine there will be higher heat output so running the AC certainly increases the heat.
Much like with the difference between coolant temp and oil temp providing an indirect measurement of the oil cooler's efficiency, the exhaust temp provides indirect measurement of the turboshaft temperature - the real reason for cool down. Because there is no direct measurement of the oil temperature at the turboshaft or of the turboshaft itself, you need to provide an ample opportunity for the turboshaft to cool below the flashpoint of your engine oil or you will coke that oil. The temperature will be different for different types of oil, the synthetics having higher flashpoints typically. Note that the concern is NOT for the oil to catch fire (not using autoignition temperature here), but the temperature at which the oil could burn if vaporized; flashpoint. The turboshaft spins at tens of thousands of RPMs at maximum boost and is supported with a nearly frictionless floating bearing lubricated and cooled by the thinnest of oil films. It is quite possible for the turboshaft to have a point temperature of nearly the exhaust temperature. If the oil is dirty it will oxidize and coke earlier but once the engine is shut off, there is no pump to continuously circulate the oil over the turboshaft (even when it is not spinning under load) and cool the turboshaft.
What is THE definitive shut down temperature? Under the flashpoint of YOUR engine oil. You will find this on a used oil analysis (UOA) report.
Predictive Maintenance Services, Inc.
Oil Analyzers, Inc. - Oil Analysis, Oil Testing Services
Lower exhaust temperatures provide better shut down considerations for the turbo BUT nothing is universal...after all, extended idling also has negative effects upon piston ring wear. Get the UOA from one of the laboratories listed above or from a truck service center locally where you may get while-you-wait analysis.
Clean oil! Clean filters - and only OEM!