Changing the water in the smaller tank is only a temporary solution- a mere few hours before the temp is back down to being cold.. And you do not want to continually change the water throughout the day as you are stressing the fish and causing too much fluctuation in the temp.
(I don't trust external thermometers, but prefer the glass ones you place in the actual water).
Larger tanks tend to hold heat better.. but again, all that work to put in partial warm water will be for naught as in a short while the temp will even back out to what it was. And you still don't want to be doing multiple changes a day.
Mini heaters are good for 1 gallon tanks.. what is more reasonable is to just buy a 25 watt adjustable heater (Elite makes a great one..
even the "mini" 25w heater of theirs is adjustable) that can actually heat a tank anywhere from 1 gallon to 5.5 gallons.. 50w for larger tanks. I use the 25w on my 1.75g conditioning tanks as well as the tubs that I have for juvie bettas. With a little shopping you can find them for cheaper than what I posted.. that is just where I go to get mine when needed.
Bettas are fine in temps that are cooler than what is preferred.. they will live in cooler temps (above 68*), but for an all around healthier, active fish you are wanting temps above 76*F. Normal preset heaters tend to run 76-78*F, I have 1 in a 6.6 gallon where the room temp stays in the 67-71*F range and it keeps it steady at 78*F, but it's a 50 watt. I would say if under 5 gallons 25watts are enough, anything 5-10 gallons you will want at least a 50 watt.