A heat gun is really overkill. I used a hairdryer on LOW heat and a spudger. It worked very well, just have faith... It feels like an impossibly strong bond for about a minute or more and then the adhesive warms up and it just pops.

If the screen is shattered over an area where there is adhesive under it, plan on a lot of time picking at little pieces of broken glass. If you can get a spudger under the old piece of adhesive and peel it off a big pice with many shards stuck to it it saves some work. Be super careful if it's shattered right over a component like the home button cables. Mine was shattered over the proximity sensor to the right of the earpiece and I came way too close to stabbing it, hard, with one end of a shard of glass while I lifted the other.

But my phone is good as new now. You'd never know it had been repaired. Yeay!