Good advice from everyone, of course. Both Gene and Chuck are right, and their solutions often work well. Most factory contact adhesives are both somewhat flexible (often latex based) and "thermo-setting" in nature. That means they will let go when subjected to wide swings in relative humidity and/or high heat over time.
The thermo-setting characteristic can be an advantage when using the hot iron to reattach a delamination. The heat of the iron melts the contact adhesive. It flows out a little bit and then cools to a more rigid glue line than you had on first application from the factory. If you get the piece back exactly where your want it, the chances are it will stay there are better than before. The down side of all that is it will be more difficult to repair the next time, if there is a next time, because you've "set" most of the adhesive with heat and pressure. There will be less, if any, which will melt the second time.
As has been said, use a thin cloth between the surface of the iron and your repair surface. We often have soft leather gloves on, and a 1" or 1-1/2" dowel in our hand to follow the iron with good, firm pressure on the repair as we pass. The surface is hot, so the gloves help protect the hands.
Linda Heuer, Past President, Spirit of Virginia Club
Greg Heuer, President, Spirit of Virginia Club
2011 31' Classic Ltd. - The Silver Otter III
2013 GMC Denali 2500HD 6.6 DuraMax - Sierra Blanca
TAC VA-18 | WBAC 1927 - Spirit of Virginia Club | AIR 53869