I'm curious if you have some real insight on this, because my understanding is that Facetime video calls are end-to-end encrypted, and the battery drain seems to be pretty minimal even on older devices.
What's your definition of "pretty minimal"? FaceTime has noticeable battery usage in my experience, but it's not excessive. I'm not sure how it compares to unencrypted video chat, but I doubt it's much higher. Crypto is typically accelerated in mobile devices these days. I would guess that the screen and network (Modem/wifi active all the time) are the battery-draining bits, and while encoding and encryption don't help, they're hardware-accelerated. That's only a guess, though, and I'd appreciate it if anyone had data on this.
Video calls in general are CPU/battery heavy operations, I've done pretty long ones with Wire (my employer) and yes, the phone gets warm but no issues with performance (iPhone 6).