75 degrees is on the cold side, a better temp would be 78-80*
Water tends to be a few degrees cooler than the air as well, and anything under 75 is a total no no.
I suggest getting a heater and keeping the tank at around 80*, an adjustable heater with a thermostat will keep the temp steady so that your betta wont have to deal with temperature flucuations.
A 1 gallon tank is very small and needs every other day water changes. So youre better off with something 2.5 gallons or larger. A 1 gallon is not safe to heat.