The Templeton family name originated in Ayrshire Scotland, and is among the oldest surnames, in the modern sense, that have been handed down to the present generation from that country.1 It "probably derived"2 from Templeton, near Dundonald Castle, the fortified tower built by Robert II on his accession to the throne of Scotland in 1371. Dundonald Castle was used as a royal residence by the Stewart kings for 150 years.

In the Detail map, above, you can see "dismtd rly" along a dotted line.  That's an old railway right of way that used to carry coal and etc. from the mines of the 19th Century that were on down the way.  You can see that there's a still-existing bridge at the "Templeton" intersection. The compound that is/was Templeton is that black line & discolored bit under the right arm of the arrow head on the Detail, just opposite that "39."

The proximity of Templeton, South Ayrshire to the castle is clear in these photos taken in September, 2009:

A full screen view of this slideshow is linked here.3

NOTES:

1) Black, George F., Ph.D., The Surnames of Scotland: Their Origin, Meaning, and History, New York, 1946, p.765.; also: Hall of Names International, Inc., website 1999.
2) Map: United Kingdom Ordinance Survey, 2007, at http://www.multimap.com/, 2009.
3) Maps: http://www.magic.gov.uk/. Photos are ©Roger Templeton, 2009.