If the fan is on more, then it's less likely to overheat than if the fan dies!
Are you sure none of the keys has stuck down or did you use it to type your MN posts ? Do you have a cat or anyone who might have spilled liquid into the keyboard ? Sorry, just fishing for a clue about what is wrong...
As a relatively cheap stop-gap (in case something serious goes wrong with the laptop keyboard, I'd suggest popping along to a big Asda/ Asda Living or Tesco and see if you can you can get a cheap USB keyboard for a fiver or so {and a USB mouse for 3 quid or thereabouts}, or even wireless setup - Asda does keyboard and mouse for 15 quid if you hate wires)...
You may feel you won't use them but if all else fails you will have them ready, just in case. I have a number of multimedia keyboards to plug into the many laptops I've collected over the years, partly to have a standard layout even if the laptop has some keys in odd places, and no numeric pad, and partly as a backup, since some software is less easy to control without access to kbd / mouse.
If you don't have any shops nearby and / or don't want to buy anything extra, there's an 'on screen' keyboard under Accessories / Accessibility on most Windows PCs, and the laptop 'mouse' should get you by (sorry, just that I detest most of those laptop sensor pads)