Most fans connected to the CPU heat sink have the speed regulated by the running temperature of the CPU. There is either a thermistor or a diode which responds to the different temperatures which is usually located at the base of the CPU. The hotter the CPU gets, the faster the fan runs. If your fan has been increasing in speed I would suggest looking inside the case to see if you have a build up of dust inside, especially inside the fan and heat sink on the CPU. If it is dusty, purchase a can of inert air to blow it out with, you can place a pencil through the blades of the fan to stop it form spinning while you do this. Before you handle any of the components inside the case touch the metal of the case to discharge any potential electrostatic electrical charges, these can kill components on the boards.
Great response. You could also try to purchase an additional or different heat sink to cool the chip.
Also, you could elevate your computer, if a laptop, on two slender wood blocks on each side, to let air pass beneath the computer to allow it to run cooler. You might get an additional fan for the computer also .
Heat problems can be fairly easily solved.