Some manufacturers do put a seal on the computer which voids the warrenty if opened, however they are normally easy enough to peel off and replace after

Cleaning your gfx is usually a matter blowing into the fan a few times and the dust should rocket out. If your card has a dual slot cooler try blowing had into the exit slot too.

If you have a stock cpu cooler (which if its OEM you will) usually the only way to clean properly is remove the cooler, unscrew the 4 screws on each corner of the fan, revmoce the fan, vacuum/blow/wash the heatsync outside of the case and clean fan with damp cloth. Then replace and your done.

As for it overheating in the start if you have a dual slot cooler on your gfx card i very much doubt that will be the case without overclocking it, and TF2 isnt exactly the most CPU intensive game in the world.

Even if your pc is a heat trap (like cillit bangs old one), it would usually take 4 or 5 hours of continuous max load at standard speeds to overheat.

Have you recently updated you drivers? If not do so, and if yes, roll back to the previous.

What card does your pc have in it?

If its a high spec ATI card (4850, 4870, 3850, 3870, etc) IT may go well over 110 degrees and not be in the red. Their designed to run ok stupidly hot :P