Won't a solid cover to make it humid also make it too hot with the sun shining on the enclosure? I keep my outside enclosures (Russians and Desert Tortoises) humid by just spraying the enclosure. I also have an underground hide that is humid where they go when it gets too hot for them. If it were me I would just make a cover out wire just to keep predators out of the enclosure.
Don't cover it. There is a real danger that he'll cook.
If you can raise the walls of his table (or provide him with a different one for outdoors) you can deepen the substrate. Deep substrate will hold moisture & provide humidity & coolness for him to burrow into.
Hi, for our outdoor tort-tables I only use a burlap tent for cover. It gives a decent shade and you can wet it with a spray. I am very aware of our heat.
I cover half of the tort table at about a 18" above the substrate, both sides are open for air circulation and if it is too hot I wet it to bring temp down. All torts seem to like it.