Running a computer in a HTPC setup is not really a demanding task so unless you are experiencing problems that simply cleaning out the heat trapping dust does not resolve, I suspect you are fine. I have had many of those fans (typically little 40mm fans) go and have simply removed the fan to allow greater access to the heat sync and had no problems. This assumes you have good front to back air flow through the case. The "System" temp is often that of the chipset so you can check your temps there with a hardware monitor such as CoreTemp, Speedfan, or Motherboard monitor - or the monitor provided with your motherboard.
Also note that motherboard designers place the chipset to take advantage of air flow from the CPU cooler. So if you are using the OEM cooler with your CPU, you may be getting sufficient flow already.
If you are concerned, measure the fan and buy a replacement fan. Try to avoid removing the heatsink, breaking the bond of the thermal interface material. Make sure you unplug the computer from the wall before digging in to remove the +5V standby voltages present when all ATX PSUs are plugged in and master switch on back (if present) is set to on.
Also, those fans are typically secured by screws that cut their own threads when screwed in. This can and often does result in small metal filings falling on the the board whenever you screw in, or remove the screws so care must be taken to remove any before applying power.
Another option is to replace the heatsink and fan with a new heatsink only, such as this Zalman
. The concern then is removing the old heatsink. Many heatsinks used on chipsets are secured with adhesive thermal interface materials and simply pulling on the heatsink can damage the heatsink, and/or motherboard. To remove the old, you need to run the computer for a few minutes to heat up the chipset adhesive, then quickly power down and unplug the computer, touch bare metal to discharge any static, then twist the heatsink back and forth without pulling on it to break it loose. You have to be quick because the heatsink is working hard to get rid of that heat needed to loosen up the adhesive.