Here is one explanation:
But we accept what tradition tells us. There is, to the west of Jericho, a mountain that rears its peak very high. Tradition has it that Satan led Jesus to this peak and showed him all the countries of the world. If we climb this mountain we can view all the neighbouring countries. This mountain is known as the "Mount of Temptation." '
http://www.datanumeric.com/vlm/07-97/8.htmHere are other explanations:
2. The temptation to take the kingdoms to Himself would have been far more powerful if it came from within Christ. Jesus’ mind would have been full of Scripture, and in His afflicted state of mind, caused by His fasting, it would be tempting to misinterpret passages to enable Him to use them to justify taking the easy way out of the situation He was in.
Standing on a high mountain recalls Ezekiel being shown what the Kingdom would be like from a high mountain (Ez. 40:2), and John, seeing “the holy Jerusalem” from “a great and high mountain” (Rev. 21:10). Jesus saw the world’s kingdoms as they would be in the future (Lk. 4: 5), i.e. in the Kingdom, when “the kingdoms of this world are become the kingdoms of our Lord and of His Christ” (Rev. 11:15). Maybe He would have thought of Moses at the end of 40 years’ wilderness wandering (cp. His forty days) looking out at the Promised Land (the Kingdom) from Mount Nebo. It is emphasized in Daniel (Dan. 4:17, 25, 32; 5:21) that “the most High ruleth in the kingdom of men, and giveth it to whomsoever he will”; Jesus would have known that only God, not anyone else, could give Him the kingdom. Therefore it would not have been much of a temptation if an evil monster claimed to be able to give Jesus the kingdom, when He knew only God had the power. However, Jesus knew that it was His (the Father’s) good pleasure to give Jesus the kingdom, and it must have been suggested by the “devil” within Jesus that He could take that kingdom immediately. After all, He could have reasoned, God has delegated all authority to me in prospect (Jn. 5:26-27), to the extent that He had power to both give His life and take it again (Jn. 10:18), although ultimately all power was given unto Him only after His death and resurrection (Matt. 28:18). Jer. 27:5-8 and Jer. 34:5-8 in the LXX speak of how God has made the earth and will give it (Gk. doso) to whomever He wishes; and these are the very words of the 'satan' in Luke's record: "I will give (doso) it to you... I give it to whomever I wish". One could say that this is a way of explaining how the Lord Jesus was tempted to 'play God' and seek equality with God- which temptation He refused (as Paul points out in Phil. 2).
http://www.realdevil.info/5-8.htm
Topic: The curious case of Miriam and her brother