Depends upon the car.  The newer convertibles with multi-layer tops are
reasonably well insulated; however, the older ones...dating from @ '92 and
earlier are fairly thin canvas (realistically) and will not keep the cool
in/heat out as well.  Also, the newer A/C systems, on the water cooled cars
(1999 and newer) are much improved, and you get much better cooling to start
with...so....everything works better.

I've got an '88 911 with one of the older tops and in Houston...also hot and
sticky, it's "adequate"...not to mention the A/C system as a whole being
just "adequate".

Hope this helps...