Hi Iain,
Dust is always a problem and should be cleaned out on a regular basis. Please don't take a Vacuum Cleaner to your pc's guts though, it can build up static and fry your components. Use a soft paint brush to clean fans etc. You should do this at least once every two months. Be carefull if you are new to this as you have to remember its gonna be expensive if you go at it like a bull in a china shop.
Is your Processor AMD or Intel? Some of the older Intel Chips had crap thermal compound on them. Also AMD's can be troublesome when not getting enough air! You may want to ensure your CPU fan is being efficient as some times the compound that sits between the CPU and the fans heatsink can break down. Get a new tube of Heat Sink compound from your local PC supplier and replace it yourself if you have the knowledge. (Remember to be carefull when removing the old compound)
Otherwise take it to visit your local PC World. They will give your PC a thorough service for quit a reasonable cost. (If anything at PC world can be called reasonable) Make sure you explain your issues and concerns to them to make sure they cure your problem.
Don't automatically think that this problem is directly linked to your Processor, many of your PC's components heat up with more use. I have to be honest, your description above sounds like it could be a Motherboard problem or GPU related. What Graphics Processor do you use? Does your Motherboard have temprature settings in the BIOS? If it does, it can Monitor your CPU's core temp and warn you when it is getting hot? Are you overclocking anything, especially your Graphics Processor? (GPU) This is a common cause of the shutdown you describe, usually if your processor is getting to hot it starts performing poorly before finally going in to thermal shutdown. GPU's only have these sort of features on top of the range models.
I would start by doing the following:
1. Carefully dust out your case and fans
2. Power up with the side panel missing, run up FS9 and make sure your fans are all operating. (If your motherboard has a North Bridge and/or South Bridge fan, these are the first ones to check as they are smaller and less efficient. Also check your Graphics Card, Radeon X800 cards had a lot of fan problems, but only later GPU's have fans fitted.
3. Defrag your Hard Drive and run Scan Disk.
4. Shutdown your PC. Wait a while and reseat your RAM. (Carefully remove it from the slot and replace it, it will clean any corrosion from the contacts)
5. If nothing else works, attempt a short prayer followed by large amounts of begging to enable you to get a new PC which will run Windows Vista and be ready for FSX when it arrives!
Hehehe, Sorry about the last one, Hope you get your problems sorted. I also have a very tempramental system but that is because I over clock it and run raid drives.
Good luck!
EDIT* (Sorry, I was so long composing the above that Cyriel gave you the short answer before I could add this hehehehe!)