I don't think the heat is going to be necessary. Would probably even make it too pliable.
Maybe warm it up just a little bit, then slowly push it into place. No, it won't mess up the paint, unless its more out of alignment than we can tell. Looks like a few degrees, max.
Add me on Steam, same name
R.I.P. Zawarudo, may you OC angels' wings in heaven.
If something appears too good to be true, it probably is.