Have you (separately) tracked water temperature?
Sadly, no.
I've also thought about the possibility of the water reheating the naphthalene (since it's temperature should be stable during freezing point and water was still hot), but the time it took from the formation of the first naphthalene crystal and the reheating simply doesn't match. Look:
-The experiment started at 0s, 98ºC;
-It took 540s (9 min) for the first crystal to appear, at 78,9ºC;
-For the next minute, the temperature continued falling (albeit slowy), down to 78ºC at 600s (10 minutes);
-At 620s the temperature bumped to 78,3ºC, then to 78,5ºC at 640s and 78,7ºC at 660s, and remained there until 720s, when it resumed the cooling.
To my mind, it's ok to assume that at the start of the experiment the water's temperature was greater than the naphthalene's. But it's also ok to assume that once the naphthalene started cooling down, the water's temperature and the naphthalene temperature's should've been close, since the tube was sealed and the only way for the sample to exchange heat was through the water. When the naphthalene started to solidify it should've stayed on it's freezing point range while the water continued it's natural cooling, having no business reheating the naphthalene.
I know I can be wrong, and if I am, please correct me!
I'm still looking foward to any suggestion!