I've just received the box-set for Christmas and started watching the series for the first time since the late sixties; it is really noticeable that all the cast are perspiring constantly - it must have been hot in the studio.
Back in the '60s film stocks were much slower (e.g. they had a much lower sensitivity), so they needed much more lights to illuminate the scenes. Also, lighting equipment was much more quaint back then, they did not had the Kino Flos they're working with today, but they used large and heavy Fresnels only. Those lamps became very hot after many hours of usage and eliminated a lot of heat. I guess they used at least fifty of them to light the large Time Tunnel set, so it must've been unbearably hot in that soundstage.
"A voice from behind me reminds me. Spread out your wings you are an angel."
Yes, I heard that anyone who was encased in any costume like Bob May who played the Robot on "Lost in Space", or the stunt guys that played aliens or monsters on the Irwin Allen series had to bare unbelieveable temperatures. Many of those full-body monster suits meant a guy was encased in two or three layers of foam rubber and/or laytex and the heat made them sweat like pigs! I'm sure cans of deodorant were needed by the caseload back then!