Deep ground temperature is reasonably easy:
At 15m down, all daily + seasonal fluctuations have nulled out, only longterm values matter. The temperature is the annual average of the AIR temperature of the surface above it. Surface type/color/texture/seasons do not matter.
For example, a black surface rock will bake warmer in the day, yes. But at night that same rock will radiate the heat faster.
Going any deeper, increase the ground temperature by 2.5C per 100m of added depth.
This is due to approaching the hotter interior of the planet, and adding a thicker layer of insulation above.
If the surface is under significant water(more than a shallow pond or marsh), skip the air and use annual average WATER temperature.
If in a region of geothermal activity, add X, where x varies wildly according to local conditions. Obviously, digging at Yellowstone will make for warmer tunnels.
For your query: the type of desert does not matter.
Just take the average air temperature(!not! average of hottest per day, you need to average of the temp over the whole day. This will be surprisingly LOW for a desert!)
And add 1.25C - 3.75C
Example: near the middle of the Sahara desert, the average annual temperature is about 16.2C
(no, seriously! I said deserts are cold! Day peak air temperature could be 38C, but nighttime drops to -4C !)
So your tunnel at 100m under it would be at about 16.2+2.5 = 18.7C
Measured soil temperatures at depth. (this is in Indonesia, but same rules apply for deserts)
(image source: https://www.researchgate.net/figure/Temperature-variation-of-underground-soil-with-depth-for-typical-days-in-Malaysia-15_fig3_256838899)