Depends on what linear means. If the excess energy is constant - e.g. 25 Watts - then certainly the LENR reaction rate is independent of the current cooling T.
I don't think that the excess heat production in the figure from Russ George's blog can be very constant. If you look at the shape of the gold coloured region in that plot it seems to suggest that the lenr-associating heating turns on slowly and then turns off slowly. It also seems to suggest that the lenr-heating is increasing as temperature declines .. which is possible but odd.
Note that the labels on the figure only say that excess heating is "25+ watts" over 2.5 hours.