I also have recently done a routine, monthly water change last week and tested his water and it's all good.
When exactly did you do the water change and how much of the water did you change?
I'd bet that his lethargic behavior is more due to a bit of shock from such a huge change in water parameters, rather than from adding a heater. Bettas are resilient fish, so he did OK for a little while with the monthly schedule, but eventually such a lax water change schedule will catch up and make him sick. So, definitely increase the frequency of his water changes. The sticky thread with "oldfishlady's water changes" in the title will point you in the proper direction.
I know that you said you are very attached to the little guy, and you are already doing a lot of things right - the 2.5G tank, knowing the water temperature, and getting a heater for him. So, up those water changes and consider getting him a filter (if he doesn't already have one) and you should be able to have him with you for a good while!