Yes, but this will vary amongst aircraft types. Looking at the limitations for the A380, the temperature is an eye watering 54ºC.
The performance will be massively limited. In more normal conditions, you'd be able to take off out of Adelaide at MTOW of 572 tonnes. But, at 54ºC, the weight would reduce by over 100 tonnes. I'm sure the ground crew, amongst many others, would give up long before that temperature.
It's entirely possible that any flights that operate out of Adelaide at heavy weights, will be adversely affected even if the temperature is in the early 40s. The 787 out of Perth becomes weigh limited at quite low temperatures, and is probably one reason why that flight departs at night. Out of Melbourne, the 93 to LA becomes temperature limited in the mid to late 30s.