The temptation of Jesus was about whether Jesus would chose to live under the Law or the new covenant.
The “devil” there is his personal struggle whether to adopt the Jewish ways or his Father’s way.
Turning stone into bread is a temptation to use the Law to please God.
The temple is where you offer sacrifices according to the Law.
The mountain Satan took Jesus to was Jerusalem. It was an offering to make him the high priest. The king of the Jewish world.
There is a very interesting documentary about a group of priests who go to the same desert to fast and be tempted by the devil.
It’s a program hosted by Morgan Freeman. In search of God. Season 3.
The conclusion was that the devil is in our hearts. Not out there in the desert.
Hope that helps.