PaulS:
Who recommended that? They should be fired.
I'm going by the specs listed here for model #MCPE-241-14-15. Notice, near the top of the page, where it says "Suggested current = 0.7 X Max".
Perhaps it means something other than what I thought it meant?
Current is pulled, not pushed. The cooler will pull whatever current it needs. Your power supply needs to be able to supply that amount of current.
I see. In that case, I presume 6A is simply the minimum the power supply should be able to handle? What's the "suggested current" bit about, then?
First thing you need is a way to measure the temperature, and humidity, in the cabinet.
Already have those.
The cooler may be PWM controllable, or it may not. If not, you would just need to turn it on and off at some interval, experimentally determined, that prevents the device from freezing.
I've read that power cycling isn't good for peltier coolers, in the long run. I've also read that peltier coolers should not be controlled via PWM.