Tiree (like most of the UK stations) shows a loop form in the sun-temp scatter plot.
Here the previous month’s sun data is plotted vs Tmax. The colder half of the year becomes flattened to nearly linear, whilst some phase lag is still evident in warmer end of the cycle.
Two month lag reverses this situation, ie pushing winter into opposite phase.
As can be seen in the non lagged plot, there is more phase lag in warmer months.