I’m not an expert in this field but few months ago I’ve been playing with non-contact power transfer.

I agree with the points made by Ionnis and pedja089 and add few notes of my own:

Your LC circuit and its Q factor will determine your frequency needed and your efficiency.
For the same setup your duty cycle will change the power input / output ratio drastically.
In your case you should draw no more than few tens of milliamps. If your outputs are getting hot you are drawing too much and inefficiently.
I’m not sure what kind of diagnostic tools you have on your bench but an oscilloscope and a variable frequency generator will be more than helpful. Monitor the output signal from your Mosfet with the scope and change the frequency until you get maximum output level, cleanest signal shape and minimum current draw from your power source. If you don’t have an oscilloscope just by monitoring the current draw will get you close to optimum. You want to stimulate your circuit with its resonant frequency for best results. Once you got over this step start changing the duty cycle of the driving signal with the same goals in mind. As we discuss in one of the treads I started in about two months ago you can use a low caliber PIC to create your output. Dealing with low frequencies will also give you access to a wide duty cycle range.
The shape of the signal driving your output device (try to make it as square as possible) is extremely important. The amplitude of this signal is also important. Try using TTL level Mosfets or use a Mosfet driver. The Mosfet driver made all the difference for my application and it is TTL compatible. Most of the Mosfets available have the needed diode built in.
If you are using audio type transformers your optimum frequency should be really low.

HTH

Regards,

Nick