The temperature envelope is there to inform you that safe operations have been proven within those limits and providing you obey any caveats written into the Flight Manual. Routine operations outside these limits may be possible but be careful, you may find that your insurance company will take a view on whether or not their cover extends to such circumstances. Also, if you are trying to be professional about the operation and verify by prediction (using Flight Manual data) that you can achieve any particular performance level (Cat B, Cat A etc) then you will find that no data is available outside the temperature envelope. Extrapolation is not allowed so once again you are stuffed!
I can identify with your dilemma having operated a 365n with data only available up to 40 deg C. What to do when halfway through the flight you find the afternoon temp climbing to 45?
If I interpret your particular dilemma correctly you are talking about taking off from a platform where the flare is producing an increase in the air temperature over the helideck. In these circumstances the received wisdom is to limit the helicopter weight when the wind is in the 'bad' sector. You are not alone. Such problems occur everywhere in the offshore world. It's like making an approach in North Sea temperatures and arriving over the deck to find the climate there is very tropical!
In the UK the operators have cooperated to produce a "Helideck Landing Limitations" guidebook that tabulates every helideck in use in the North Sea and around the UK (platforms, drill-rigs, drill-ships and vessels) to advise the pilots an the restrictions to be imposed on any particular helideck.
More info available from the British Helicopter Advisory Board. see
www.bhab.org