IMO/E.... the gradual temp fluctuations over a period of time are generally tolerated by a healthy Betta-be it due to day and night temp or the varied temp within the tanks different levels that are normal...... especially in tanks without water movement and under objects in the tank.
In my tanks the temp can vary by near 10 degrees at different levels especially under plants-I don't use filtration and/or water movement in my tanks 10gal and under and even with the fry I have not had any problems
In the summer the Bettas I keep outside and their eggs/fry have tolerated well over 100F and high 50F short term-with day, night and rain causing both gradual and sudden temp swings without issues, however, my Bettas may be tougher than most and I do feel that overall general heath, age, genetics and diet has a big role in how well a Betta can tolerate temp swings both gradual and sudden-be it extreme or slight....
Sudden extreme temp fluctuations can be stressful even for a healthy Betta-that said-most can still tolerate it without any long term effect, however, it not recommended and should be avoided if at all possible.
Bettas are a lot more tolerant of temps than they are given credit for IMO/E....of course this can vary based on several factors......overall health, age, diet and genetics....