Yes, as Miles says, the heated air charge will be less dense, so less oxygen, so less fuel proportionately to be burned.
Bob is right too. My carbed 4 cylinder Lycoming has poor fuel distribution, so it is leaned until the leanest cylinder can still fire well. That leaves 2 cylinders running somewhat lean, and one that is still pretty rich.
Adding carb heat for high altitude cruise warms the fuel, so there are more gaseous fuel molecules, which flow with the air, and less liquid fuel droplets, which can condense onto the intake manifold which becomes 'wet flow' and may not follow the air flow in proportion.
This condition (Carb heat on, leaned mixture) "might" make as much power as no carb heat, (leaned as much as possible while still running smooth) because a rich cylinder does not make full power. It probably won't, but it WILL be using less fuel.
The 2nd option is to close the throttle a little. This tilts the throttle blade in the carb and re-directs the air/fuel flow into the intake manifold plenum.
For my Thorp T-18, above 4500' msl, this is the combination for range. Carb heat on, 3/4 throttle, leaned. I lean until power just begins to fade, then add back enough to keep the power. The EGTs are much closer, and the engine runs fine. Yes, some speed is sacrificed, and the air cleaner is bypassed, but for a long trip up high where the air is cleaner, the economy and slightly more relaxed place can be worth it.