The decay heat will be an issue for quite some time. Folks don't realize how hot those rods really are. I believe in an earlier post I made mention these guys need more support. This isn't like putting a hot pan in water and a few minutes later it is cool to the touch. Although, that doesn't mean it is not under control either. This is going to take weeks to work through.
How long does it take to cool down a reactor? There are design specific variables there. The easiest way to answer that question is that NRC regulatory requirements for emergency power supplies is that they be available on the order of a month. You can render a plant in an acceptable condition within a few hours. However, heat is still being generated. If you had to stop, at any point, carrying away that heat, it would start building up again. Emergency cooling systems have to be available for weeks.
Ping to link in #54
Weeks on a partial meltdown. TMI to 5-6 months to cool.