Is there a soil temperature that is too hot? I checked the temperature in my 16" containers at the end of the day when the air temp was still near the high of 96F. In the center of the pot six inches down, the temp was 90-95F, while an inch from the edge I found a high temp of 108F.

Hello,
commonly the roots won't suffer, if the temperatur won't stay above 102°F to long.
Because amino acifs get damaged at those temperatures.
Roots seem to cool themself by little loss of water, so if the temps get tp long that high, the roots will get 'boiled'...
But if the roots stay betwen 95° and 99°F, it should be optimum for best root performance, if you haven't grafted to Poncirus trifoliata... because the later rootstock is much better adapted to cool temperatures, so will get root problems if the tmeperatures rise to long and to quick above 93° F...
Many other Citrus rootstocks just get best growing conditions, if the soil temps rise above 90°F and stay around 93°F......
If the roots heat to much, simply shade the pot with some bright colored cloth....

During the summer, and at times even during the cooler temperatures of spring and fall, a black colored container setting in the direct sun can reach temperatures in the range of 110 to 120F. The root on the sunny side of the container will die. When pulling the tree's root ball from the container the damage is easily seen. You can help prevent some of the heat build up by painting the container white, to reflect the sun's light away. - Millet

Millet,
because of very low temperatures in spring and fall, I usually recommend dark pots to ensure heating up the rootball by sunlight, which ensures good root temperatures, even if surrounding air temperatures stay below 68°F...

So to ensure that roots won't get 'boiled' I hang white cloth from the top of the pot down, so prevent that sunlight will reach the pot and heat it up, and this works...

So, painting is one idea, but difficult to remove, cloth is the other one, which needs some effort to set, but is easly removeable on demand

Steve, that certainly would work. I paint one half of the container white and leave the opposite side black. During the summer I turn the white side towards the sun, then rotate the black side of the container towards the sun throughout the winter months. One could also simply set a black container inside a larger decorative container to avoid overheating, giving a higher decor appearance to a patio or porch. - Millet

Millet,
nice trick... but I use only small pots, so painting the pots will look some what funny.. and guess about my wife... She lives now with someone who has a citrus arboretum at the windowsill... think what she might guess, if I paint the pots only half

So I use the thing with the cloth, because my wife tolerates that more