WPC Inductive Power Transfer
Cut out the middle man and control the heat with a simple circuit at the power-receiver-end. That's how I would do it because it keeps the control loop stable and requires very little wasted power to do this.

I have designed multi channel data monitoring systems in applications powered this way and I'm a strong believer in autonomy at the receiving end!

If you do need to send off some data then there are several ways that this can be done using independent low power rf systems. If you do need an uplink to the receiver then amplitude modulating the power carrier does work and is simple to demodulate.