Take some liners from some old boots and put them in.
If you have to use your actual liners then take them out of your boots when you done, stuff them with a towel and hang them upside down to dry.
DON'T put them on a radiator! I haven't done this myself because I think it's bad for the liner. Here's why:
Most boot liners seem to be heat mouldable to some extent. This makes me assume that the foam in the liner is designed to 'creep' (engineering term for tendency of a material to slowly stretch/deform under low force). In order to make this happen the liner will be made with a foam designed to become creep at and above at certain temperature (the Glass transition temperature, Tg). Below this temperature the material will not creep/mould much. Above this temperature the material will creep much faster. The Tg is not a precise temperature for these materials, its a temperature range and the higher the temp, the faster the creep process.
If you put your liner on a radiator and its heats up to its Tg (and above) then the material will try and return to its original moulded shape from the factory rather than the shape to which it has adapted to (i.e. your foot). Not good.
If you have foam injected liners then I think this will be less of a problem (I'd imagine that the foam in these liners is not meant to creep and has a higher Tg). But I still don't think its a good idea to use these liners. I don't know what type of foam is used in injected liners but if its an open cell foam (I'm guessing it is) then water will get into the foam. The foam walls will absorb some of the water which plasticises it (reduces the Tg, makes it less stiff and strong) and will break down more quickly as a result.
NB If the foam in injected liners is closed cell then jumping into water shouldn't have much of an effect.