I don't do well in very hot places and swore I wouldn't ever go to somewhere like Rhodes ( which can be very hot, more so than some other Greek Islands) in the middle of the summer. Yet I found myself there, a good number of years ago, in the last week in July for a free holiday as my daughter was a holiday rep there, with a Greek Boyfriend whose relative owned a Greek Travel firm, at the time. Hottest day was 45 degrees. I survived and enjoyed our holiday, but some of it was spent under shade and with plenty of water and other drinks, high factor sun-cream etc - especially in the middle of the day ( say 11am to 3pm)
I would avoid Lindos altogether if I were you. It is down a steep road to the town/village and is so sheltered that it is often so much hotter than the other tourist villages on the east coast. I got out of my Daughter's air-conditioned car and got an instant headache from the wall of heat which hit me as I got out of it.
You might not want to stay at the hotel every single day, but if you want to do any sight-seeing at all, hire an air-conditioned car? It made a huge difference that my daughter could drive us around the whole island in hers. Prasonisi, in the south, where the Aegean and the Mediterranean seas meet is the windiest place and therefore a little cooler. Our timing was great. You could literally stand with one foot in the Aegean and the other in the Mediterranean as there was still a strip of sand between them and you could feel the difference in the water temp.
I would avoid any trip to Embonas too, as that is high above sea-level in the mountains and was VERY hot the day we went
Just take GREAT care with the suncream. Daughter loves the sun and the heat, spent a number of years as a holiday rep on a number of Greek islands and never got sunburnt using Factor 20. She is currently in Kos, and got sunburnt lips and part of her tummy, using Factor 30, which surprised her
Go and have a great holiday. Just take care