I can think of a few places where you have desert and forest near one another.

You may or may not get the TYPE of forest you want but these can serve as models for you to work from.

1. Basically all of Peru and Chile.

2. The Black sea's southern coast line.

3. Basically the entire southern border of Tibet.

4. (and 5) are both from Utah actually. The first is a ten minute drive from Salt Lake. The Salt flats are nasty hot. But I think #5 is the closest for you. The national forest is beautiful the mountains are amazing...as soon as you hit St. George completely desert and dry, and a little further south once you drop through the virgin river basin you hit the desert outside Vegas and that is truly desolate.

Notes:

• Elevation will have to play a role, generally a mountain range. Its the only way to get the temperature swing necessary to support the two environments.
• Proximity to water. If you want trees you need water. Mountains help make the distribution of that water uneven.

These are the two key factors to get what you are looking for. But as mentioned in other answers, the temperature swing in deserts from day to night is larger than in any other habitat, you simply don't have anything to stabilize it (water, trees, etc)

I can think of a few places where you have desert and forest near one another.

You may or may not get the TYPE of forest you want but these can serve as models for you to work from.

1. Basically all of Peru and Chile.

2. The Black sea's southern coast line.

3. Basically the entire southern border of Tibet.

4. (and 5) are both from Utah actually. The first is a ten minute drive from Salt Lake. The Salt flats are nasty hot. But I think #5 is the closest for you. The national forest is beautiful the mountains are amazing...as soon as you hit St. George completely desert and dry, and a little further south once you drop through the virgin river basin you hit the desert outside Vegas and that is truly desolate.

Notes:

• Elevation will have to play a role, generally a mountain range. Its the only way to get the temperature swing necessary to support the two environments.
• Proximity to water. If you want trees you need water. Mountains help make the distribution of that water uneven.

These are the two key factors to get what you are looking for. But as mentioned in other answers, the temperature swing in deserts from day to night is larger than in any other habitat, you simply don't have anything to stabilize it (water, trees, etc). Water also helps normalize temperatures a bit.