I may store a cpu and cooler in box for a few days because I will take a mobo to pc shop to repair it. I must re-apply a thermal paste on cpu for reinstalling it on a mobo ? I use a intel stock cooler and bought it a few hours ago.
Always best to re-apply paste after you remove the cooler from the CPU, re attaching it without reapplying the paste will leave air bubbles and areas where the thermal paste is thicker, overall decreasing thermal performance.
I have seen some cases where you can get away with it, but it can depends on the wattage of the chip and the load it is given.