I've finally got round to doing some tests on the rod donated a while back by tk8456 (John). My initial test was to measure the modulus of a section of the (broken) rod between two set point temperatures. I chose to measure between -20 deg. C and +55 deg. C and measurements were taken at a frequency of 1Hz.
Anyway the answer I got was that modulus (stiffness) reduced linearly by ~0.1% per degree C. I guess the temperature range over which most people actually fish will be more like 20 deg. C, so they'll most likely see a 2% change in modulus. Whether this is detectable in a fishing situation is open to question.

I'm expecting to see a bigger effect when I get round to testing fly lines.

Great work James. I guess 2% is nothing in anything but the most demanding conditions on a rod.

Be very interested to hear about lines.