Are you somewhere in the world with access to a bird vet? Get him in ASAP. for right now do as you would with a burn on you: run cold water over it immediately to stop it burning and to relieve pain.
The vet will likely give antibiotics. Burns get infected very easily. No ointments or anything like that, it will just trap heat and cause more damage.
Water, call Vet for Appointment, Water, Water, Water, take Budgie to Vet, Water and Medication supplied by Vet, Water, Water, Vet Medications, Aloe Vera.
I'm a big believer in Aloe Vera, but with a burn, keeping the area clean comes first.
You can soak the foot in dilute betadine and water. Just a drop or two to lightly tent the water. Hold foot in fir a few minutes if your bird let's you