Toad-Man wrote:
The way turbine engines work mean that as the air gets colder (perhaps due
to low surface temp or climbing to higher alt for example) they become more
efficient and generate more power for a given power setting. The 'laymans'
(i.e. my!) logic for this is that since turbines work by heating air, the
cooler the air at the intake, the more the air can be heated by the engine
thus producing greater thrust.

This is part of it, the other part is the flame temperature in the
engine is much hotter, because the air is less dense while you use
approximately the same amount of fuel to generate as much power (or
thrust in a jet engine). So you not only have cooler intake air, you
also have much hotter turbine inlet air.