We stayed in a bell tent near Sarlat about 10 years ago with the same conditions, and it was terrible. We had 250 steps to get to the car park so if you wanted to do anything you had to do it early or late. We ended up doing out on day trips just to be in the air con of the car. I finally cracked at 2am one night and booked a hotel in Paris with aircon for the final 3 nights and we left first thing the next morning.
I did a market 2 days ago, on Sunday in the steaming heat, luckily we were in the shade but the people who weren't were pretty unhappy.
I froze 2 milk bottles refilled with water and used them and some frozen blue picnic ice packs to keep my ice box cold. I also froze made up squash so that as it melted I could have cold drinks all day. I took some cloths so that if needs be I could wet them and use them to mop my brow/wipe hands etc. Frozen stuff is key to survival.
I didn't walk in the sun at all, either to or from where I parked unless i had no option. The key thing is to stay out of the sun at all times. Open one front car door and the opposite back door and waft the front one several times open and close to pump the hot air out and park in the shade whenever possible.
Do stuff early and late and sleep for the afternoon. Buy a rechargeable small fan, you won't regret it.
Spray the bottom sheet with water just before you get into bed, it will help to cool you down. Take a spray bottle or 2 with you and fill it reguarly.
Keep hydrated, stay out of the sun and find a lake or beach to cool down in.