I red here that people use a meat thermometer instead of a regular (cheap) ground thermometer. Any reason for that? I'm planning on buying one to keep my containers from overheating during these hot days.

I bought a digital meat thermometer for around ten bucks that quickly measures soil temps. It has a huge range, something like freezing to 400F. The mechanical ones have a range limited to actual meat temperatures, though.

Not sure of accuracy but I've read they should be fine.

Thanks for the information! But why does every one use a meat thermometer instead of a soil thermometer ?

Seven, they don't all purchase meat thermometers. I use soil thermometers, to test my containers, and actual soil. In fact I have 4 of them. - Millet

Just bought a soil thermometer this morning. It really amazed me how hot the containers are when it's not even noon yet.
I measured 30°C on the side facing away from the sun and the side that was headed towards the sun goes up as high as 36°C.
I've put the meter about 10cm deep and between the rootball and the potedge.
So I think it's fair to say that at 10cm depth, the temperature in the middle will be around 33°C which is the maximum it is supposed to reach before the roots get inactive. The temperature lower than 10cm in the middle (the lower part of the rootball) I guess is a bit lower than 33°C.

Would anyone recommend shading the containers during the hottest part of the day?

The temperature range for citrus root growth is between 78 to 90F, 79 - 80F is best, above 95F root grows stop, and at 105+ citrus root growth can die. - Millet

My 5gal pots are painted white on the sun facing side, AND the pots are mostly covered by a wall and I see about 90F on hot days with the meat thermometer