I drove my '31 Roadster today from Los Gatos (southern SF Bay Area) to Lake Berryessa and back for some jet-skiing with my son. That's 225 miles of driving round trip, in particularly hot weather - about 95ºF for most of the drive. With the top down, hat on, and a bottle of water at the ready, it was manageable. I didn't prop the windshield open (as mine is a bit fidgety), but that could have made things cooler.
Air conditioning systems can be fitted, and I have seen many in hard-top cars.. However, for such to be effective in an open car, one would have had to have the top up, and side-curtains on. That is something I do when driving in very cold weather - which for me means less than 35ºF. With that set-up, due to incidental engine heat, one can be comfortable down to about 10ºF. As such, in order to provide good cooling, in addition to being top-up and side curtains on, I expect one would want to have a thermal firewall insulator added, to prevent the A/C from just fighting the engine heat.
(link to example firewall insulator below - no commercial connection to me)
https://www.quietride.com/product/fi...-Insulator.pdf