A few thoughts that might help (at least I hope so)......
The Peltier soda can coolers and even the larger tote versions do work quite well.
But they are, again, horribly inefficient as heat movers.
Reliable yes, light weight yes, rugged yes, efficient......um, no.
In those applications they also are cooling typically smaller well-insulated spaces/items and they are not adding more heat actively as the cooler operates.
So eventually, they will indeed cool down the target item, but at a cost.
I built a detached garage around three years ago and was very concerned about how hot it might get inside.
While we are in a relatively mild climate, it does top 100F routinely in the summer months.
So this was no idle concern.
The solution was radiant barrier insulation added to the underside of the roof and wall exterior sheeting.
An air gap was left between that and the sheet rock interior (no batting or foam- the air gap is critical).
It works very well.
It is not "cold" inside, but it is usually 10-20F cooler inside than outside.
And because the extreme heat of the exterior coverings baking in the sun is not re-radiating into the interior, it feels even cooler than that.
You can test this very easily by covering a small south-facing wall section with aluminum foil and comparing how it feels to stand behind it and an adjacent un-foiled section when the sun is beating against them.
FWIW, it might help your A/C work better.
As far as the FT-5 is concerned, at the hot end, hot is better,
The extruder motor should probably be kept cooler (hence yet another justification for a Bowden type extruder) and definitely the electronics.
There used to be an old rule of thumb that for every 10C higher temperature in operation, the service life of components such as electrolytic capacitors is halved.
So +20C, 1/4 the lifetime, and so forth.
A more practical approach however is just to try to keep everything under about 40C.
As for humidity, I am probably the wrong person to answer that.
It is not generally very humid here, but others on the forum have experienced swelling of the melamine parts in high humidity areas such as Florida.
And at least in theory the raw filament can absorb moisture as well and cause issues.
Other than that I am not aware of any components in these kits that should be particularly susceptible (most everything else is made from plastic or rust-resistant metals).
I hope this helps.
Perhaps someone else who has had humidity issues with these printers will chime in.