I was making roux last night from lard and flour and as I stood there stirring, listening to God Music and drinking a Harp, I wondered what was going on in the pot in terms of heat transfer.
First, there would have been almost no temperature variations within the roux. My stirring made sure of that. So the roux was of even temperature with two boundaries - one of the pot and the other of the air. The pot, being cast iron, wasn't quite even in temperature, but probably close enough where it contacted the roux. Same with the air.
Consulting an engineering table, I discovered that lard is almost twice as easy to heat up as water. It takes 1 calorie per gram of water to raise it 1 degree C. It takes 0.54 calories per gram of lard. I'm way rusty on my heat transfer calculations, but to me that says the lard would have been closer to the temperature of the pot than the temperature of the air as compared to what a pot of water would have been.
I'm discounting the effects of the flour suspended in the lard, which is probably a tragic mistake. Flour needs only 0.38 calories per gram to go up one degree Celsius. That suggests roux - an even mix of flour and lard - would be closer still to the temperature of the pot.
Maybe Ohioan at Heart or Mut could lend a hand here. They're a lot closer to the worlds of science and engineering than I am right now.