Ah, a chance to use something from my old chemistry courses!
<Geek mode ON> If it really is Bakelite (phenol-formaldehyde resin), it simply cannot be reshaped by heat because it is a thermoset, not a thermosetting plastic.
<Geek mode OFF> Fortunately there is an easy way to test if something is Bakelite and it isn't risky.
Hold the buttplate under your running hot water tap for 30 or 40 sec, then smell it. I'm not kidding!
If it is Bakelite it will be unaffected except that it will smell pretty strongly of phenol which to me is sickeningly sweet and tarry (some may think paint remover or varnish).
Other plastics won't start smelling AT ALL with this mild level of heating will not do this - and they probably CAN be reshaped with a bit of heat.
/John