st3v30 :
It wont randomly shut down.Paste is there for better heat transfer between CPU and cooler.If you dont put paste, your CPU will be few degrees hotter.
If you don't have any thermal paste between your heatsink and CPU, the heat transfer will be so poor that the heatsink might just as well not be there as the two surfaces are usually far from perfectly flat and have almost no heat transfer. Thermal paste fills in those gaps to compensate.
The 7700 already runs close to 80C due to the thick thermal paste between the die and IHS. Not using thermal paste under the heatsink will easily send it beyond its ~100C thermal trip limit when under load.