Ambient seems to low...
That said, my ambient is between 74 and 77/78 most times. Can dip as low as 72 at night during winter.
I like enclosed racks. I do believe it absolutely helps to keep the temps more even. Most people will say UTH doesn't help to warm the ambient, and in most cases its probably true (cages, open racks) however, when I pull my tubs open, I can absolutely feel warmer air coming from the tub. My rack has one single heat tape that snakes (no pun) its way under each tub, up the side and under the next tub. So each tub has heat from below and a bit from a side.
Temperature of 60 degrees or in the 60's is going to be a problem, though, unless you heat the whole room or keep enclosures that will raise the ambient temp.
Also, "if" you ever have to treat your racks/enclosures and surroundings for snake mites, that may be a problem for the birds. Most of those treatments are "sprayed" and I know birds can be extremely sensitive to things like that..
Can your birds handle a ambient temp of around 75 degrees if you heat the whole room?
Can you remove the birds temporarily if you ever had to treat for mites ? (until the fumes dissipate)