Hi,
When mosfet's first started to become popular back in the 1980's i had designed an amplifier using power mosfets and op amps as the mosfet controllers. The mosfet gate voltage changes with temperature so it's easier to NOT try to adjust the gate voltage to get the right quiescent current flow to avoid crossover. The trick is to design two voltage followers, one with an N channel and one with a P channel, the N channel putting out a tiny bit higher voltage than the P channel, then put them together with small resistors between them. The quiescent current then becomes a function of the two small resistors rather than the gate voltage. The N channel stage sources the output current and the P channel sinks the output current, so we get full wave operation similar to a good bipolar design except there is almost no crossover distortion.
For example, with a 0.1v offset in the N channel amp and 0.5 ohm output resistors, the quiescent current flow is 100ma:
Iq=Voffset/(R1+R2)
That virtually eliminates all crossover distortion.
We must also be aware that this is still a linear amplifier however, so there will still be high dissipation in the two transistors.