how to calculate value of capacitor and inductor in a high power LC circuit?
You do not need to drive it with a conventional AC switched H bridge - you want net DC of one polarity for heating and of the other for cooling. 

You can eg turn MLB on DC and PWM MHA to get one polarity, and eg MLA, MHB for the other. Effectively you have a buck converter. Vdc = Vdd x duty cycle. 



TI SLOA023 - Reducing and eliminating the Class D output Filter 

Related

Of use, but your load is non inductive, so not wholly applicable.

Fres = 1 / (2 Pi sqrt(LC))
 Impedance = 2 Pi sqrt (L/C)

Useful

Wikipedia - Class D amp