Cuprajake Not that I know of - obviously they are not paying the bill to heat up Westminster Palace (which I bet is a fair amount), but while they get some accommodation cost allowance (£18-25k depending on location), it does not specifically cover energy costs. Then again, if you are making well in excess of £100k including all the allowances, plus various other perks, an expense increase of £5k gross a year is probably quite bearable.
EDIT - the allowance does cover the energy costs, but there is a cap on the total (see paragraph 2.11 in the IPSA document linked above).
The other interesting thing is that £420,000 over 3 years is actually a fairly modest amount. 405 MPs have claimed (according to the same source above), which makes the average claim £350/year per MP.
This is not to say that the government is handling the situation well (or is handling it at all). However, I think that attacking ‘the privileges of MPs’ on this is the wrong angle.