Actually, we normally do see increased economy from Cold Air Intakes, because the motor is running more efficiently. Same reason we see better economy from free flowing exhaust systems. The more efficient the motor is running, the better its economy and the better its performance.
Been modding cars for 17 years, and have had V8s in 4000lb sedans get over 30mpg on the highway. No stocker could do that, but a modded motor can.
Any Turbocharger or Belt driven Blower has a built in heat source, it is called the heat of compression. When you compress a gas it builds heat which in some applications is great enough that the blower or turbo requires an intercooler to keep it from overheating.
As for warmer air giving better mileage, that is true to a point, warmer air is less dense at any given pressure than cooler air. Less density means less free oxygen for combustion which in a fuel injected application means less fuel delivered in order to maintain a proper fuel / air mixture that will fall into the combustable range for that application. But as the density of the air charge decreases so does the available horsepower which helps mileage up to the point where the engine can not provide adequate power to maintain a constant speed.