It is interesting that this thread has concentrated on performance issues. In high or low temperatures the physical limits of the machinery can be of more concern than the performance.
All aircraft have environmental limits.
The Bell 206L3 has a max ambient air temp of 51.7c (125F) and I can say from first hand experience flying in temps around this limit has one concerned about Gearbox temps/oil temps etc.
The R22 has a stated demonstrated limit of 38C at sea level due to cooling issues. Again first hand experience of oil temp on red line when operating a standard R22 in the tropics. Look at R22s used for mustering and you will notice they have been fitted with a larger oil cooler to aleviate some of the problem. What are these high ambient temps doing to other lubricated components.
Take off performance may be the least of the issues of operating in high ambient temps.