Polystyrene begins to soften at about 100C and melts at around 200
-240.   With that in mind I put a piece of low density blue XPS
insulation foam in the pressure cooker briefly, then depressurized it
and quickly clamped it in a vice between two boards that had also been
in the pressure cooker.    I squeezed it to about 2/3 it's original
thickness.    (from 1" to 1/2"), and allowed it to cool.

    The result was quite interesting to say the least.    Of course
this process put the blowing gas under pressure, but didn't break the
cells of the foam.   The resulting foam is extremely resilient compared
to the original.  The original will dent with hard finger pressure, and
retain permanent dents, and it snaps very easily. The compressed foam
flexes under finger pressure, the depression covering a much larger
area, and less depth, and recovers it's original shape very quickly.  It
will also form around a surprisingly tight radius, forming wrinkles on
the inside face which come out gradually when the pressure is released
and the foam straightens out.  It is a far tougher foam than the
original product.  It's observable that the outer surface is denser than
the core...... due to the very brief heat cycle.  This was the object. A
dense surface with a low density core.  The idea was to have a
progressive change in density with the outer surface being the most
dense.   There was no breakage of internal cells evident.... even under
a magnifier.
    Most interesting is that a room temp "control" recovered to near
it's original thickness without any apparent damage where pressure was
uniform across the piece.   A second piece crushed down to about 1/4"
thickness from it's original 1" returned to about the same thickness at
the hot crushed foam, and also retained it's integrity, and exhibited
identical behavior.... great resilience and flex compared to the original.

    My conclusion here is that the heat did allow the foam to reshape
permanently..... It didn't rebound significantly.   The results were
positive.   A much better foam resulted.  More heat is needed.  Probably
a sheet of foam compressed between two steam heated platens, similar to
a plywood making hot press to about 1/3 it's original thickness using a
process where the foam was compressed over a time period, then the
platens flooded with cold water and the foam allowed to cool slowly,
would result in an impressive product.   The blowing agent (gas) is
retained in the cells, and is now under pressure, resulting in a springy
behavior. Even at 2/3 it's original thickness, it's a foam I would not
be afraid to use in some situations.     The original density of this
foam I believe is 1.3 pounds per cubic foot, as compared to Divinicell
at 5 pounds per cubic foot.   In essence this means that this product
would have to be compressed to 1/4 it's original thickness to weigh the
same.  (actually .263%)

    Obviously nobody here is going to build a steam platen press to
compress foam.  The other factor that is interesting here is that the
cells in the foam would then have about 40 psi pressure..... assuming
they started out at atmospheric pressure..... The effect of this
pressure is evident even compressed to 2/3 it's original thickness.  
This I believe accounts for the resilience of the foam after
compression.    There is likely a point of diminishing returns
somewhere.   The internal pressure is obviously an asset.

    Of course the ambient temp of the environment where a compressed
foam was used would be a big concern.   A dark colored boat in the
tropics might develop enough heat to cause expansion of the core....
probably not a good thing.    Below the WL, the resilience of the foam
due to it's internal pressure in an impact situation could be an asset.

                                                            H.W.