The typical lapse rate on Earth is about 6.5°C/km. That's why it may be a cozy 20°C at the surface but below -25°C at the summit of Mt. Everest.
Extrapolate that in the opposite direction, and the bottom of an ocean-free Mariana Trench would be almost 70°C warmer than the surface. Therefore, regardless of pressure, the temperature would be approaching 100°C, and be completely deadly. Even if that may be inaccurate depending on exactly what insolation the Mariana Trench gets and how circulation changes, the column of GHG above the Mariana Trench would be several times more than on current sea level. Valley bottoms can get very hot already today: Death Valley in the USA is less than 100 metre below sea level and temperatures reach above 50°C. It doesn't take much more heat than that to be more immediately deadly.
If you were to drill a 10 km hole on land, it would be deadly hot as well, not due to the lapse rate, but due to geothermal heat. The bottom of the 12 km deep Kola Superdeep Borehole was expected to be 100°C, but instead found to be 180°C. In deep underground mines within the Arctic Circle, miners can work in shirts and shorts year round (as far as temperature is concerned).
If the Mariana trench wasn't underwater, it means all the oceans have evaporated, which would only happen as a consequence of a runaway greenhouse effect, which means we're all dead already anywhere on Earth anyway. Or even if we succeed to make the water magically go somewhere else than the atmosphere, its absence would cause a very extreme climate, in particular at such deep and dry spots.
All of the above is a simplification, as the entire climate on Earth would dramatically change. For a more sophisticated answer (still simplified, but less so), one could run a climate model with the oceans switched off, and see what happens. I don't expect the bottom of the Mariana trench to be a pleasant location under those circumstances