It depends on which desert! Please rewrite the question to ask about a specific desert,
Deserts can be found from below sea level to above 10,000 feet elevation such as in the Ladakh of India.
There is no 'typical' altitude. Deserts can range from well below sea level to thousands of feet above sea level.
Please name a specific desert.
Not all deserts are hot. Compare the Sahara with the Gobi. The Sahara is hot and dry and also is located near the equator, with an altitude of about 600m. The Gobi is much further north, with an altitude of about 1520 m. The Gobi is COLD and dry.
The Ladakh is a high altitude desert in the Himalayas so is quite cold the year round,
The Simpson Desert of Australia is a hot desert.
The Mojave desert does not have much altitude, but if where ever is closest to the sun and out in the open is the hottest.
Hot desert
The Gibson Desert is a hot desert.
Yes it does. The higher the altitude, the cooler the temperature in general.
A hot desert
The Arabian Desert is a hot desert.
The Kalahari is a subtropical hot desert.
The Kalahari is classified as a hot sub tropical desert.
The Arabian Desert is a hot desert.