They do not use the money for building temples. If a temple is built, the LDS who are within the area of the temple are each sent a bill for their share of the cost. I am a Catholic who lived in Bountiful, UT for 9 years. When the South Jordan temple was built. Each any every LDS in my neighborhood was sent a bill for their share of the cost (the money was not considered part of their tithe).
As I understand it, only tithing members are allowed in the temples, but the percentage is much higher than 15%. You must tithe in order for your marriage to be "sealed" in the temple, and you must be "sealed in the temple" in order to be a god of your own world after you die.
The 15% is the figure for the temple recommendation. There is a list of stuff you must swear to in order to get the TR, tithing is only one of the items.
The temple has several areas, it is the inner circle the is prohibited unless you have a TR.
Billing for the buildings, makes you wonder what they do with the tithes.