Hi pukka7773. I have no experience of this machine, but I'll share a few thoughts on the problem. You have installed a software application, which I guess is monitoring the computer temperature. If the temperature you are monitoring is that of the processor, then 46 degrees is not excessively high, but 59 could be a problem.
Laptop computers usually (I think) use the baseplate to dissipate the heat, and some do this more efficiently than others. If your computer is overheating at high ambient temperatures, ten ensuring a free flow of air over the base, or standing it on a surface that is good at conducting the heat away, could help the situation.
If your laptop is within its warranty period, then I think the behaviour you describe makes it unfit for the purpose for which it was sold, and therefore PC World may not be being helpful, but they are responsible, so don't take any nonsense from them.