Welcome to the site, Trevor! This is the best forum for ball python fans, hands down (no pun intended). Your cage is fine for a baby, but he will need something bigger as he grows, whether an aquarium or a Rubbermaid type container or a custom cage.

I understand about your mom, and it means that you should definitely monitor your temps and humidity with something reliable (digital, not those stick-on thermometers), and should probably insulate the tank as well (cardboard, styrofoam, old blanket, pretty much anything will work). Inside the house is definitely a better place for your baby, but you can probably make it work in the garage if you work at it.

Tell us more about what you have set up so far. Is he in an aquarium? Does it have a screen top? If so, is the screen covered? How are you measuring temps and humidity? What are the temps and humidity? How many hides, and what are they? How do you plan to cool him off during the summer?