to be safe and to make sure its the fan and for $$$ purposes, u can try getting new thermal paste first, and then if that doesn't work, then mayve a new fan
You should get Premium Artic Silver Thermal compound supposed to lower by 8 degrees than normal kind. Yoiu should just go ahead and buy the best CPU cooler you can find for under 40 bucks. that would be the best short/long term investment.