If you do not have any hidey hole for him, then yes the light will stress him out. Bettas are low-level light fish and bright lights for long periods of time will stress them out.

But yes, 65� is waaaay too cold, and most likely why he is so lethargic, so if the lamp is your only means of heating his bowl for the time being, then make sure he has a place to hide from it when he wants.

I agree with Mary though, you should upgrade him to something bigger that you can put a heater in. 2.5 gallons is a nice size for one betta (and especially if you don't have a lot of room for a large tank, as I don't!) and you can put a 25-watt heater in it with an adjustable thermostat. I have one of my bettas in a 2.5 Minibow (you can find these at Walmart for around 30 bucks) with 25-watt heater and it works great. We keep our house below 70� in the winter so I couldn't do without it.