Photo Credit: TJ Holmes/springcreekbasinmustangs.com
A letter addressed to the Chair of County Commissioners describes Temple Butte as a feature with an elevation of 8,600 feet and located approximately one mile SE of McKenna Peak. It was named after Pati Temple (1951 - 2013), who volunteered with the Bureau of Land Management to help manage a local mustang herd. The exact location is described as "Sec 16, T42N, R15W, New Mexico Meridian; San Miguel County, Colorado; 37°53'48"N, 108°31'50"W."
The signed letter from the U.S. Board on Geographic Names is available for viewing online as a PDF.
A map of the feature can be found on the USGS website. In the photo above, Temple Butte is the tallest feature in the background.