Yup, the heater should keep the temp just right for the betta (between 78-82*F) all year long. So you shouldn't have to worry about waiting.
As mentioned above, just make sure to acclimate him properly to both temp and chemistry, by floating his cup in the tank for 20-30 mins, and every 10 mins or so take out some of the water from the cup (dump it down the drain) and put some of the tank water into the cup. That way you avoid the risk of putting him into shock from sudden temp/chemistry differences.
Make sure you have a thermometer to tell the temp for the tank, and once it's at the correct temp, then it will be fine to put one in =) Good luck!