Structure of My roof:
I have Big Wedge Roof that has Flat roof attached to it.

The flat roof on my front and back porch needs to be redone.
In addition I also need to get a small flat roof redone on my main roof that is attached to the main wedge roof.

I called in two roofers and both of them are giving me two different ways to do it.
Constructor 1 - hot solution and they will torch and do it.
Constructor2 - Cold treatment, he said that if i go in for torching it might engulf flame inside wood of my old home and cause fire.

I live in north NJ very close to NY.

1. Which one to go for hot or cold solution?
(if it depends on my location's Weather Conditions).

2. What are the benefits of each at my location- northern nj?