Why do piston engines have a lower fuel consumption with higher temperatures?
I don't have a reference, but the physics behind is not that complicated.

The key is that you have constant RPM, constant pressure altitude and constant manifold pressure.

A motor sucks in lots of air, but since the throttle restricts the air flow in the intake, the air pressure between throttle and motor is low. This is the manifold pressure1. At idle, i.e. almost closed throttle, the pressure is very low, while at full throttle, it ideally equals ambient pressure. And in turbocharged motors, it is even higher than ambient pressure.

Finally, manifold pressure together with RPM and displacement of the motor is a measure of how much air volume is aspirated by the motor per time interval.

Since you keep everything constant, this volume also is constant. But warmer air is less dense and contains less oxygen molecules per volume. 
Less oxygen molecules means less fuel can be burned. This is why fuel consumption is lower.
But it also means less power. To compensate, the throttle could be opened a little more to let in a little more air volume. This would also increase the manifold pressure.
But if the throttle is already fully opened to get max. power, you can't open it further. So, max. power is lower at higher temperature.



1) NOTE: For simplicity, I'm speaking about absolute pressure here. The gauge in the cockpit displays the under-pressure with respect to ambient pressure, so a high displayed value means a low absolute pressure. And since ambient pressure changes with altitude, manifold pressure does, too, even if the displayed value is constant. The benefit of this is that the displayed value is a good measure of the power with respect to the max. power achievable at that altitude.