You can get underfloor heat-pads that fit like underlay under the vinyl and this may help a bit. It's quite expensive, but may be worthwhile...
I've been involved in fitting flooring in hospitals, but some products would be too 'industrial' - and can be difficult to pull up if you want to change back to carpet in the future - my favourite vinyl type product is Karndean (it is phenomenally hard-wearing and almost bulletproof) which is similar to the Rhino mentioned earlier.
Also, dont forget that you need to make sure the edges are properly sealed (clear bathroom sealant will do) to all of the skirting boards - you'd be surprised how much gunk can go under the flooring here.
Are you fitting to floorboards or a solid floor? This can also impact on the best choice - and impacts on underlay too.... (the tiles are less good on bare floorboards and may need a different approach
hope this helps
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