How can I make a sheet of metal with a mdf backing glued to it rigid, so that it does not bend out of shape ?

It needs to be something that will not add too much weight to the whole thing. I have found in certain places that are hot (over a radiator or open fire) that the metal and mdf begins to bend.

Answers:
if you must use mdf, go with a metal 'frame'....preferably on with support (ie crossmembers) on the hidden side next to the wall. otherwise try a better (or thicker) sealant over the mdf before glueing on the sheet metal.

Other answers:
rivet a strip of aluminum corner molding down the sides
rivet a strip of aluminum corner molding down the sides
You need to create an air gap for insulation. I am guessing that the MDF is geeting hot and the glue is getting soft so the saw dust in the mdf is moving a bit, or the adhesive between the MDF and sheet metal is softening up. You might want to try hard wood in stead of mdf.
I don't know what gauge metal your using, But I try a thicker gauge....maybe 20 gauge?.that stuff is hard to bend..
For gods sake lady!!! Do not put mdf over a open fire...I is nothing but cardboard.
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