I had exactly the same problem as you describe.
I was able to fix this myself, it took about 2 hours, because it was unfamiliar and annoyingly fiddley! I bought the parts - two thermostats for £10 from a 'local' repair shop. From what I’ve read the rule seems to be replace both thermostats to be safe. These components look rather like cylindrical bits of plastic wearing tin hats but one is twice the size of the other, the larger being about 2 cm in diameter, and they DON'T look identical. The part numbers (for my WD860) are: HPT 1605 160 and HPT 1604 802.
1. You’ll need to use a combination of finesse and brut force to get the lid off of the machine. It is secured by two screws at the rear but has troublesome plastic hooks inside, half way down either side, that stop the lid from riding up at the front. The process is to remove the screws and then pull back and up to ‘unhook’ the internal brittle plastic hooks. I found this scary and difficult, cracking sounds were off putting and I did break to tips of the plastic hooks a little but they still seem to work ok. Be careful and wiggle it gently from side to side is the only advice I can offer.
2. Once inside it gets a bit easier. You should be able to see a metal snail-shaped object bolted to the top of the drum with various electrical connections – this is the dryer and within it are the two thermostats. What you’ve got to do is remove/unplug all the electrical connections from the top dryer, of course, make a diagram first as you’ll need to put them all back after. You then need to unbolt/unscrew the top half of the dryer and remove this from the machine – this is another fiddley bit and I was lucky again here to have a very small ratchet socket set which made the hard to get to bolts/screws accessible. Note: some of the screws are the Torx type (imagine a more complex Phillips’s type screw). You’ll need to have a Torx type screw driver head that’ll fit the small socket tool to undo these.
3. Once the top of the dryer unit is off, you just need to remove the thermostats – one is fixed in by screws on the outside of the dryer top and the other is fixed in by screws on the inside. Screw in the replacement thermostats, then clean off the fluff and burnt fluff from both halves of the dryer and you’re there – put the machine back together.
I did this over a year ago and haven't had trouble since. Mine went just out of warranty too - what a surprise!
Mr Fixer, October 2008