yes the foam will absorb water but then you let it dry out, i did it a few times you can also wrap it with a towel and then toss it in the dryer on low heat or air dry for a while i did that also. you can also put the pad next to a dehumidifier to help get the water out, the point of the whole thing is getting the new emblem in without ripping or cracking the original pad.
the problem with a hair dryer or heat gun is the heat is concentrated to one area and usually not deep enough into the material surface. a real hot day might be rare in your neck of the woods so for the sake of speed it is an option you can try.
I honestly didn't have any issues with the repops, the reproduction ford OEM tooling for the dash pad was a nightmare by comparison.
I'm sure there were different batches of the pads made i ended up with 2 and didn't have the problems don is describing. i guess i was lucky or another manufacture did take over at some point for me this was about 7 years ago now.
some lubrication will help push an emblem into the holder.
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If your pad is dried and hard -
Coat it with a light coat of Vaseline - put it in a plastic bag - put it away for a couple of weeks / month
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if you try this don't use Vaseline, use a product like Nu vinyl, it will hydrate rubber and vinyl and you can put coat a pad then put it in a bag, however it can get into the foam and cause problems later. the effects of restoration on rubber or vinyl with this method are temporary once removed from the bag. within hours the part will return to pretreated form.
people have started to use Orange hand cleaner to treat rubber products it will soften rubber and swell silicon for an extended period of time, however if applied over a couple of hours it can damage the item you are trying to restore. time till damage is hard to know especially if you only have one of something to try it on.
people have also attempted to use transmission or engine treatments that are designed to swell rubber seals obviously this is more dangerous.
try a hot day first combined with a hair dryer wear gloves get the rubber hot and pliable then try it. if that doesn't work think about the next step.
I've used the water trick for years. I mold my own plastic and rubber pieces for restoration work and custom designs as a hobby.