To make it a little bit clearer it is not the number of electrons that flow through the coil that counts, it is how much of a tough time they have getting through.
Take a nice big wire, 10 gauge, and make it out of a good conductor, copper, use some high voltage, 110, and you have household wiring. LOTS of electrons flow through and, if you don't trip the breaker, it does not get hot.
Take a smaller wire, 28 gauge, and middling conductor, Kanthal, and some middling voltage, 3.7, and not nearly as many electrons flow but it does get hot.
In the house with the big pipe the electrons just zip through, they have plenty of room to avoid hitting each other or the stuff that makes up the wire. They arrive at the other end with almost all their energy.
In tight pipe the electrons hit each other and the stuff that makes up the wire. When they arrive at the other end they have used a lot of their energy just getting through the wire. Every time they bump something the thing they hit vibrates a little more than before and the electron looses a bit of energy. The happens a LOT of times and you turn the electric energy into heat. The wire gets hot.
The house wire also does get hot, just a tiny bit so you do not notice it and it is radiated into the surroundings about as fast as it is created. If you put too many electrons through the house wire, a short or 7 hair dryers, house wiring will get hot. In a house the circuit breaker is a weak point in the circuit and it opens before the wire gets too hot.