If this helps, Continental do a great service if you can find an approved route involving them, that suits your needs.
I just successfully brought my cat from Houston to Gatwick on Continental, who do not have a heat embargo because they take extra measures to keep the animals out of any climate conditions up until the point of boarding.
What I learned is that apparently Continental keep the animals in a climate controlled area before driving them out to the tarmac in also a climate controlled vehicle, and they load live animals the very, very last thing, as close to takeoff as possible (and also unload them first at the arrival end). In this way, they don't need a heat embargo the way other airlines impose.
The animals travel in a separate compartment of cargo which is also climate controlled with the same air that circulates in the passenger cabin. At no point are they subjected to heat or cold. I was very, very happy with Continental's care of my cat.

You do have to be careful about the "approved routes" and airlines in conjucntion with anyheat embargos imposed in some areas -- some airlines are approved but only to fly out of and into certain airports but not others. Always check with Defra -- calling them is helpful as you get the information instantly from the horse's mouth so to speak.