As long as they don't get infected you should be fine treating them at home.
Theoretically we're not supposed to pop the blisters, because the fluid provides some cushion, and it lessons the chance of infection. That said, kids nearly always pop or tear theirs...and sometimes it just plain feels better to not have this big painful blister.
NEVER put a burn in butter, oil, lotion -even aloe lotion-, or non-burn ointment. These things keep the heat in, and actually make burns worse. (The old put a burn in butter thing was from back in the days when butter was kept on ice in the celler, along with steaks, it was the cooling factor of something that was cold when cold water was not readily available. Hence also the steak on a black eye. Icepacks, before icepacks. Ice was too precious to be wasted, butter or steaks could be used/cooked. Ice had to be chopped in the winter and kept all year).
For minor burns:
- Cool/cold running water immediately after to stop (blanche if you will) the burn
- Aloe (straight, plain aloe gel) until the skin breaks
- Neosporin or other antimicrobial ointment after the skin breaks
- Allow it to breath at night if you're bandaging
- Keep clean and dry (ish...meaning don't keep wet, or go swimming) but getting wet in everyday life is fine)
- Don't submerge in hot/warm water (like a bath, or while washing hands)
- Tylenol or Ibuprofen (yup. not just for headaches & teething)
- An icepack (with a washcloth or other barrier between the skin and the icepack) can also feel nice. You only have a few seconds to a minute or so to put a burn in something cool to keep the burn from getting worse...but cool things on burn even long after the fact usually feels very nice.
If it gets infected, or if a fever develops, or if the area burned is, say, bigger than a quarter...take him in to the Ped. Otherwise, no biggie. Just make sure you check it often. I usually check at mealtimes, bath, & bedtime...or if there's some kind of "ruckus" like wrestling, or playing with the dog, or a sneaked trip to the sandbox, etc. Anywhere that it might tear or get dirty.
Mmmm...future caveat...even if small (larger than a pencil eraser, or even that small but near the eye), any burn on the face/neck/genitals warrants an immediate trip to the Ped.
If it makes you feel better btw...when I was 5 I stuck my finger in a steam pipe...and when I was 8 decided to try the "walking on hot coals" trick I'd seen on Discovery by reaching into the BBQ ash and grabbing a coal. For the first, I looked like a cartoon that has just hammered their thumb...and the second gave me a burn that covered my entire palm. My own son decided to try grabbing the hair curler from the wrong end. My best friend in the 2nd grade poured boiling water down her chest (grabbed a bowl that had been destined for instant potatoes and tipped it out on herself (that one required grafting). I have such a big family I could give you 50 stories easily...but suffice it to say...kids do these things. They get burned (hopefully mildly like your son), and learn not to touch hot things. Or at the very least to grab less quickly, and test for heat.