There is some power dissipated in the crossover and it depends on what level you are running your amp. I'm a flea watt guy and there i almost no heat generated. But I built my new crossovers with 10 to 30 watt resistors so they won't blow if someone hooks a zillion watt amp up to them. Remember for 10dB increase in volume, you need 10x the power. So if a teenager has a party you could blow the crossover...there are actually stories on the internet about this.
I don't like electronic crossovers. I hate processing the signal any more than I have to. Many readers have no such feelings. They use equalizers, ss preamp, ss amps, etc and the signal goes throught a million components before it gets to the speaker....so to each his own.
Jerry