Solid silicon, yes. Various pastes, sealants and other stuff that incorporates silicon, like the 'silicone sealant' around your bathtub, have different properties. Because more people are familiar with rubbery and squishy things called 'silicone', it's common to think of those first.
I'm reasonably confident that the OP wasn't saying it was the substrate of their chips that was causing the liquid.
I'm more than familiar with the make up of thermal paste. I'm a chemist.
First. Thermal paste is designed to get hot, it's ridiculous to assume that it's melting under conditions where the processor doesn't fail. I assure you that the thermal paste will be tested at both extremes.
Secondly, if there were a situation where the thermal paste melted, it would re-condense before it started leaking out of the computer - i assume the liquid coming off the laptop isn't at 380 F?
Third. Thermal paste does use solid silicon, thermal paste is a mixture of various chemicals NOT a compound.
Finally. The volume of thermal paste used is about 1 mL - that's enough saliva used to a lick a large stamp - not much, it simply isn't enough to ooze out of a computer.