I took delivery of a belt drive and Rohloff titanium bike (Nua Bikes, Barcelona custom design) towards the end of March 2020. I've probably done about 3000 miles on it. I did not adjust the belt, as it always felt much the same as when I got it. Not being heavy or athletic, I was sure that it would never skip over the sprocket.
However, after fixing a puncture with temperature at around 2C on 5 November 2021, I noticed that the belt no longer felt well tensioned.
Back home, I was surprised to find that only one turn on the M5 screws that move the sliding dropouts was enough to bring the belt back to specification tension. So, the difference between palpably slack and proper tension was only 0.8mm (the pitch on an M5 thread).
I calculated the thermal expansion of the chain stays, using the distance between centres of 438.5mm from the Gates app and coefficient of expansion of Ti at around 8.6 x 10 to power -6. Even a difference of 30 degrees C would only shrink the distance by 0.113mm. The actual drop from average UK summer temperatures was less than 20C.
On an aluminium alloy bike the expansion for 30C at coefficient 23.6 x 10^-6 would be 0.310mm. However, carbon fibre expansion, working in the opposite direction has a coefficient of about 2 x 10^-6.
Conceivably, a cyclist with an aluminium bike, riding in a continental climate with very hot summers and sub zero winters might find the chain significantly slack in winter if it had been adjusted on a hot summer day.
In the UK, thermal changes are unlikely to have a significant effect on belt tension. I am hoping that my belt has just taken a long time to settle to its final length and/or that very slight slackening is not detectable by casual observation until a critical point is reached. I will be keeping a close eye on it now.