Well, you really don't have to do anything. Most every CPU can easily handle temps of 10% above the thermal rating. So, for your CPU that would be 6c or a total of 67c on average. More than likely it can run like that for some time, however it will tend to shorten it's life some what.
If you do decide to run it that way, you should remove the HSF and clean the surfaces, and replace the TIM at least once a year, and use high quality TIM.
I really can't guess about how well the H60 will work. It's not much better than a decent air cooler, and it's effectiveness depends on cool air entering the radiator, and i have a feeling that will be a problem for you as well.
You'll just have to decide for yourself which is the best solution for you.
If you do decide to run it that way, you should remove the HSF and clean the surfaces, and replace the TIM at least once a year, and use high quality TIM.
I really can't guess about how well the H60 will work. It's not much better than a decent air cooler, and it's effectiveness depends on cool air entering the radiator, and i have a feeling that will be a problem for you as well.
You'll just have to decide for yourself which is the best solution for you.