I'm not sure where either of you live, but where I live watering the ground around the containers will not work to keep the temps sufficiently cool enough, even if done three times a day. For containers that aren't basic white, the temps will skyrocket in direct sunlight even in the AM here. Watering the ground is wasteful (and can be expensive in SoCal) and that dries up so fast it really only encourages weeds.

You could bury the container, even doing so 3/4 way down helps tremendously. Or paint them white. Yes putting shade cloth over them so direct light doesn't beat down on them will help tremendously, but that may reduce the light on your tomatoes /shrug. You could loosely wrap the shade cloth around the container itself -- that works fairly well but I've noticed unless the shade cloth is white, darker cloth will tend to absorb the heat and it still radiates from the cloth. Simplest? Just loosely wrap (or lean) some cardboard around it -- ugly though.

One of the best methods is to do pot-in-pot (cache pot) where you put your plastic one in a larger container leaving at least 2" of air space around it. To improve that further, put very large sized bark nuggets in that space. It will keep the inner pot cool in summer and protect it from colder temps in winter. That obviously doesn't work for self-watering containers.

I do a combination of the above ideas. For some I buy those cheap car shades from the dollar store and wrap them around the container. It reflects the light to surrounding plants and keeps the container cool.

In the hottest part of my yard where direct sunlight beats down on my container citrus all day, I am forced to use shade cloth over them all. Many plants stop photosynthesis production when root temps and/or leaf temps reach 100F. They also don't need as much sunlight light as some people think -- but I live in the Central Valley of CA with tons of sunlight.

That's the gist, but there are some other ideas in this forum as the question comes up quite a bit.

Although I am not the OP - thanks for the tip about placing P-I-P with bark chips in-between. I have been trying to start a container for carrots but could not decide how to keep the roots cool. This pot-in-pot sounds like the ideal solution.

Thanks,
DL

Save the plastic bags that potting soil comes in, cut them into strips that fit around the sunny side of the containers (like aprons). Use clothes pins to hold them in place, and have the white side facing out. The white plastic will reflect the sun, and since the plastic never fits tight, there will be a cooling space between the apron and the plastic container.