I would check the water temp in the morning (as well as various times during the day/eve for baseline). Just because the air temp hits 65, doesn't mean the water temp is 65. An article about bettas and temp:
definitely get a heater. Bettas thrive in warm water. much below 75 they become lehtagic/listless.
they actually survive in a wide range of temps from 75 to the mid 80's.
they originate in areas that water levels fluctuate but can become shallow thus subject to a wider range of temperatures.
most folks try to keep the temp in the lower 80's or upper 70's.they do make small heater for smaller aquariums.
the cable heater won't help at all for the betta, those are made to stimulate plant growth and to warm the substrate a little bit. I wouldn't think it would heat the water temp since there is no water circulating through the substrate.
"Helps increase by a few degrees Fahrenheit/Celsius the water temperature of mini aquariums compared to the ambient/room temperature where it is positioned (ready carefully instruction manual)."
Has anyone used the Hagen Aquaclear brand? They make a 25 watt that appears to be smaller then the other I have found.
I really didn't like my last experience with Hydor - had a 50 watt cranked up to 87 for a week in a 10g and couldn't get the water above 80. - It has been replaced!