Templehall seems to have been a very small place - just a single cottage by the mid-19th century. Note that James and Elizabeth were described as
in Templehall. This quite specifically means that they did not own the property - if they had, the description would have said
of Templehall not
in.
The Ordnance Survey Name Books, compiled in 1858-1861, say that Templehall was the property of Henry Houldsworth, who also owned Coltness House and various other farms in the vicinity. The Houldsworths, who came from Yorkshire, bought Coltness Estate in 1836.
Templehall is described as
A small cottage occupied by an agricultural labourer. See the map at
https://maps.nls.uk/geo/explore/#zoom=15.7&lat=55.78296&lon=-3.91739&layers=5&b=1 - Templehall is half-way between Wishaw and Coltness House.
By the end of the 19th century Templehall had disappeared from the maps. See
https://maps.nls.uk/geo/explore/#zoom=16.0&lat=55.78327&lon=-3.91769&layers=168&b=1 - but its name was preserved in the name of a nearby woodland plantation.
So it would be reasonable to suppose that James Moffat was employed in some capacity on Coltness Estate.
As for who owned it at that time, in 1760 there was an action against Sir James Stewart of Coltness, and there are earlier sasines mentioning Sir Thomas Stewart of Coltness and his wife Susanna Denholm. (Maybe that's where James M and Elizabeth S got the name of their daughter born in 1765?).
