Baby bettas do need to be in warmer water, as well as a bit cleaner water then adults and their food needs to be really really good quality/live- Petco doesn't tell you that when they sell those baby bettas. What you do now will effect it's life span and overall health throughout it's life. Even the cooler water will cause lowered metabolism and immune system.
They may still grow up without the proper care for a juvenile, but it will cause trouble for them as adults.
That being said, you have a cutie! A bit older then most of the babies they sell, as yours is already a bright color.