surprised you didn't get answers
we had friend who was too cheap to buy outdoor rugs when her grandkids were big enough to walk around the pool on their own
she bought the spongy shelf/drawer liner and made pathways
didn't last long

then she hired someone to resurface her poured aggregate decking with a cool type of acrylic...that helped a good bit...
since most outdoor rugs are made from poly materials they are likely to get hot too...don't know how hot though...

suggest your look at Houzz website and search for outdoor rugs...
probably some ideas there...you might have to create account to search...don't think you had to do that in past but looks like you do now...