The temperature range would be greater on the land of a desert.
Deserts generally do not have enough water to support a forest so your question is an oxymoron. Deserts and forests are separate biomes.
Water is evaporated at any temperature but a high temperature favors evaporation.
temperature, water and elevation
Water is evaporated at any temperature but a high temperature favors evaporation.
Water remains a liquid over a large temperature range.
desert
The warmer the temperature, the more water vapor the air can hold.
230
109 degrees
All that water near by.
Anywhere below freezing, or 32 degrees.
Not all deserts are hot. The Gobi Desert in Asia is an example of a desert with cool or cold areas. The term "Desert" does not refer to the average temperature of this biome; it refers to the lack of water and limited precipitation it receives.