The weather is hot and humid here, much like in Florida.
I have my Groomer cut both mine at a #7, which is about
1/4" length. I'd say that is the "bare" minimum for length.

(excuse the pun)
However, on their undersides chest/breast on back...
I SCALP them !! We go on jogs, and they love to briefly
rest on the cool grass under a shade tree, and having that
direct skin contact with that, really helps cool them down
when they need it.
Another favorite cool-down place is the wet area beneath a
few of the Water Fountains on the Jog Trail. Both mine are
totally etiquetteless, and don't mind plopping down in mud at
all. Fortunately, with the short hair, a simple rinse with cool
water when we come back home, gets them houseable.
However, on the other hand, I've found that Yorkies for the most
part, are somewhat cold natured regardless of their hair length.
So, at home in the A/C, I make sure that they have fluffy blankets
in their bunks, where they can curl up overnight/naps.