Postman, The rule of thumb with heat bending wood is...dry wood, dry heat. Wet wood, steam.
If your staves are still a bit green, take the bow down to floor tiller stage and clamp it to the caul and allow it time to dry. Be sure the back is well sealed so it doesn't check while drying.
The heat gun I bought about 10 years ago was $5 at a garage sale. I believe it is 1200 w max. You don't have to spend a lot on a good heat gun and you don't need the best. Pat