Depends on the concrete. Peak concrete temp for a fully exposed location on a 95-100F day is around 120-125F and maintains that for about two hours. On either side of that peak is a sharp drop off into the 90s and 80s. Blacktop, red bricks, or colored concrete can easily hit 140F+ and maintain "burn yo ass" levels for 4+ hours. For reference, you can fully submerge most plants in 120F water for an hour or two and not do any serious damage to them (though I don't recommend over 111'ish).
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For the concrete to do serious damage to your root system, the concrete itself would need to be radiating more than 120 degrees for much longer than a couple hours per day. It would first need to dry the dirt in your pot and then bring the ambient dirt temperature of that dirt up over 115 degrees for an extended period of time. Small plants might roast on a sidewalk from evaporation, but any plant with a decent amount of dirt should maintain just fine through hot days as long as you keep up with the summer watering. I have left potted chiles on the front and back sidewalk in 90+ degree full sun every day for years without a problem. If you have multiple 100+ degree days in a row and you're sitting black pots flat on concrete, that could be an issue due to how much heat the pots themselves absorb from the sun. Easy enough to offset by wrapping them in not-black towels and/or putting a buffer of some sort between plant and concrete (towel, sand, etc).
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Now...as for me, anything over 70 degrees is too hot. I sweat rivers at 72. Summer down here is mentally retarded.