The upgraded cooling was probably a BIOS flash which made the fan run semi-permanently rather than just occasionally. Tends to reduce the battery charge life
Its worth considering that this IS a well documented problem, and on SOME models HP unilaterally extended the warranty period, but I don't believe this is one of them
However, it does give you leverage against HP or Dixons -if you want to play hard - in that the machine was sold with a manufacturing fault and so they have a liability under EU law
Howver I've not yet met anyone who has had the persistence to take anyone to court over it. In this case it would have to be Dixons as they are who you have the sales contract with