This is necessary only for the most revered sites and I carry my 'legs' if indeed that's on the day's list when I have people in town. For most temples, shorts that approach the knees and a shirt covering the shoulders is sufficient. The bigger show of respect is not wearing ratty clothes or beach attire etc.

More attention is paid to a woman's clothes than a man's and I have seen women, both Thai and foreign, told not to enter temples due to their attire much more than men.