The MOS technology is voltage driven. Logical gates in a static state carry virtually no current. Nor does the input of the next gate. This is their main advantage over older technologies such as TTL that are current driven. The only current the gates consume in a static state is a leak current, measured in nA (nano-amperes) or less.

The situation changes rapidly on a transition between states. It takes a finite time for the top transistor to open and the bottom one to close (or vice versa) and during this transition both transistors are briefly partly open, causing a brief current spike. It is very short, lasting a tiny fraction of the clock pulse length, but it is non-zero. Furthermore, the input of the next gate acts as a tiny capacitor which needs charging or discharging every time the logical state changes. Again, the capacity is minuscule and so is the charging/discharging current, but with millions of gates on a chip it all adds up.

You can imagine that the more logical state transitions per a unit of time, the more both of these effects are noticeable. Hence, higher clock frequency = increased overall current consumption = increased heat.