The hard cap on temperature is placed by solar irradiation and Earth thermal radiation. To make a place hotter, a location solar irradiation for the day need to exceed the combined thermal radiation for both day and night.

CO2 helps capture some of that thermal radiation but even at 500ppm it's not doing that much. And all of this is not considering the movement of air and the effect of ocean which tends to act as a huge circulating heat sink.

The hottest place achieve those temperature by: not being next to water/plants, having no air movement, and sun directly above. The only param that changed with time is small amount of CO2 concentration, the effect on the maximum temperature on Earth should be minimal.

It's the wild swings in random location, change in weather pattern that will be more trouble. That and the rising sea level.