Here in Tucson Arizona where we regularly fly in temperature variations between 68 degrees and 105 + in the summer time during one morning flying session, I have noted several things (possibly) at least partially related to prop pitch and temperature.
First as, everyone knows, as the temperature begins to climb in the early morning it is necessary to lean the mixture of the engine or add nitro to maintain a given RPM...no surprise there. However, I've found that to maintain the same lap times it is typically also necessary to increase the engine RPM by as much as 250 to 300 RPM at the extremes of those temperatures. My guess is that this is due to the decrease in air density and it's effect on thrust from the prop. This means of course that the air temperature effect would be a greater factor in speed than the decrease in drag on the airplane and lines.
It may also be partially (small amount) due to the general loss in power and change in torque curve of the engine.
I have also noted that this effect seems to be more drastic with two blade props than with three blade props, but seems to be unrelated to whether the engine is piped or muffled Some or all of this may of course be due to the difference in efficiency of the individual props but the difference is significant and very noticible. (all props in question are carbon)
I would mention that here in Tucson the humidity is typically very low and doesn't change significantly from those low temperatures to the high extremes. Typical numbers are less than 10% relative humidity, often as low as 3-4%.
There are a few times later in the summer (late July and August when the humidity goes significantly higher but I haven't done any testing during those times. I suspect that the differences if any are small due to changes in humidity.
During that time the nitro flows freely!! 25% to 30% isn't unusual.
With that much nitro it's usually necessary to open the needle even at the higher temps.
Randy Cuberly