Which are you trying to control - temperature or humidity?
Have you researched humidors? An oversize humidor seems like what you are trying to create.
There's no PWM needed here, or putting it another way there's no reason why you'd need to switch the peltier on/off more than a couple times a second to keep a reasonably stable temperature.
"Significant precautions must be employed with PWM, however. First of all, the PWM should be at a high enough frequency to minimize thermal stresses to the TE devices. While we like to keep the frequency in the low killihertz (Hz) range, in many applications these days we must compromise at around 120 Hz for the sake of electromagnetic compatibility. Another important issue is the potential for generating electro-magnetic interference (EMI) in the wiring to the TE device. If you are using PWM, you may need to shield your power wiring or keep it away from any sensitive electrical signals."