If it's hitting 80C you're well outside the CPUs normal operating range and need to do something urgently.
That type of cooler (I'm assuming it's the stock Intel design) uses plastic pushpins that are known to loose their holding power over time so it's likely that's the problem Try pushing down on each in turn to check all four are still down tight, if they seem solidly attached changing the thermal paste would be the next logical step.
If the pins seem loose the Arctic Freezer Pro 7 and Freezer Pro 13 are, as I recall a straight swap, pushpins and all, takes longer to clean off the old thermal paste than to install and they're a bit better than the stock item. Plenty of other coolers exist, but for a simple, non overclocking swap they're great.