With “absorb,” “deflect,” and “channel”, you’re talking about three different material properties.
To “channel” refers to thermal conductivity. You want materials that are good thermal conductors, like copper, silver, aluminum, and the like. Heat sinks are typically made of these materials because they collect heat from a source and move it up to fins that have a lot of surface area to transfer it to the surrounding air.
To “deflect” refers to thermal resistivity. You want materials that are poor thermal conductors. In fact, one of the best insulators is no material at all: vacuum. If you’re really serious, you get a vacuum with a few loose layers of thin aluminum foil; the aluminum resists radiative heat transfer, improving even further upon the vacuum. For something less exotic, consider refractory bricks, which tolerate high heat and offer good insulative properties. This is in fact an extremely porous collection of silica fibers, so it is in fact similar to the silica gel you mentioned. A variation of this material was used in the space shuttle’s heat shield.
To “absorb” refers to a material’s heat capacity. This describes how much thermal energy is required to raise the temperature of a material by a certain amount. On a mass basis, hydrogen is pretty tough to beat, although it’s difficult to work with because it has such low density unless you pressurize it. On a volume basis, water is among the best.
So you want a desiccant that’s a good thermal conductor with a very low modulus of elasticity. I don’t think there’s a single material that fits all three specs.
A layer of silica gel won’t dump heat to the atmosphere better than the bare surface of the HDD, unless you’ve deliberately shaped the silica into a heat sink, i.e. a geometry that has a lot of surface area (i.e. fins) through which bulk air can flow. Such a geometry is likely to be fragile; mechanical shock will be absorbed by fracture, meaning it won’t be much more useful than a bare HDD.