Totally agree with Meatpuppet, get a heater, the light won't provide enough and at nigh the temp. drop will shock the fish for sure! Bettas that are too cold won't eat because their metabolism shuts down. Also make sure you supply a hiding place like a plastic cave with no rough edges or a silk plant, bettas that are stressed because they have nowhere to retreat to don't eat either. Also agree with Meatpuppet about the filter, the less disturbance the better.
What are your water parameters? By that I mean pH, ammonia, nitrate, nitrite, and chlorine levels. If you don't know, go get a test kit. If your water parameters are unsafe, the fish will get sick or poisoned.