If it's just bits of white coloration on otherwise normal looking fin tissue, I think he's just coloring up for you since he's been home. This is not unusual. If the texture is somehow different, for instance, if the area is fuzzy or fluffy, then it might be cause for concern. Otherwise, I think he's fine. :)
Fin rot occurs (usually) when the ammonia level is high enough to burn away the delicate edges of the fin tissue. The wounds caused by the ammonia burns become infected by bacteria and turn gray or black with a crusty texture. New healthy growth often shows up as clear to whitish, and is a good sign.
You should consider returning your heater and exchanging it for a better one. If it is one of those non-adjustable pad heaters or a pre-set heater, it's not going to be good enough. You need one with an adjustable knob because the one you have now just isn't cutting the mustard--bettas should be kept between 77-83 degrees. They are cold-blooded, so being kept in cool temperatures can cause circulation problems, digestive issues, lethargy, and a crippled immune system.
I use and recommend this 25 watt heater: http://www.fosterandsmithaquatics.co...8&pcatid=11368
-- when/if you do get a new heater, it's important to set it just above room temperature initially, then slowly turn it up a degree at a time about every hour until it's at the desired temperature.
As far as your water changing schedule goes, I'm not sure that it will be enough. General rule of thumb for a tank near that size is a 100% change every 4 days--if you got some live plants like java moss, for instance, you could stretch that a bit. Since you're new to nano fishtanks, it might be a good idea to either purchase your own home test kit like this one: http://www.fosterandsmithaquatics.co...54&pcatid=4454
or take a sample of your water to a local pet store once a week for a few weeks to make sure that your routine is really getting your tank as clean as it needs to be.
You should also consider switching to a high quality pellet brand instead of flakes. Pellets are generally higher quality and are easier to digest than flakes. I recommend Atison's Betta Pellets, Ken's Betta Crumbles, Omega One Betta Buffet Pellets, or New Life Spectrum. All of these are good brands, and it's good to alternate between a couple of different pellets, along with frozen foods that are available in the freezer in the fish section of most pet stores. Variety ensures that your betta gets proper, more complete nutrition and fiber.