This is just plain old physics. The amount of calories burned is based on the amount of work it put in.
Work = Force x Distance
Force = Mass x Acceleration
So based on that, you can put in more work (thus burn more calories) by either moving more mass at the same pace, moving the same mass at a faster pace, or both.
10,000 joules of energy (Work) is equivalent to roughly 2 calories.
For example, say you had a 100 kg sled. You were able to push it at a rate of 10 m/s^2 (because you're extremely fast and powerful).
100 kg x 10 m/s^2 = 1,000 Newtons (N)
1,000 N x 10 m = 10,000 joules or roughly 2 calories.
Of course this is a very simplified view of the whole picture. Pushing a sled is harder than running. Running is harder than cycling (on a flat surface). There are other factors that go in to play like friction, surface angles, wind resistance if you're outside, etc.
The point I'm trying to get across is the amount of calories that burn is determined by the amount of work that is done.
Regarding heartbeat, this can be a way to measure the amount of effort a person is pushing. People who have been working out for years will be more efficient than people just starting out, so they will burn less calories for the same work. Likewise, experienced people will also have slower heartbeats because of how relatively efficient they are.