Not sure if you're asking about steady-state or dynamics (or, that's precisely part of the confusion).
Heat flow depends on the temperature drop across a given volume. So, the component heats up, which heats up the grease, which heats up the particles, which heats up the heatsink. No heat flows until the temperature rises, at least by small increment, and so on until equilibrium.
Thermal impedance does depend on the heat capacity of materials involved. The grease layer of course is very thin so can be ignored for this purpose, but in general everything has thermal mass and conductivity, and therefore some diffusivity which describes the rate at which heat spreads out over time:
https://en.wikipedia.org/wiki/Thermal_diffusivityThere are two kinds of flow here:
Heat flow is a steady-state condition, when one thing is hot and another is cold and there's power dissipated. The power and temperature values are static, but we still say a power is energy in motion, a flow. In thermodynamics terms, this is a quasi-steady-state condition, because it's nonequilibrium (heat is still flowing), but nonetheless no variables are changing.
"Thermodynamics" itself is a bit confusing or unintuitive, because what's "dynamic" is the "therm", the heat
energy -- not heat power. Nowadays we mostly use "dynamics" for time-varying systems (e.g. differential equations), so it can seem strange that thermo deals with steady equilibria. Typical thermo problems consider a start and end condition (e.g., pressure, volume, temperature, energy input/output), and don't care about how the system evolves between those end points, so long as the end points are stable equilibria; or more particularly, that the system can only evolve in specific (and most importantly, continuous) ways between those points, and in such a way that the rate doesn't matter (expanding a volume of gas in a perfectly insulating cylinder, changes its temperature adiabatically, no matter how fast or slow you do it).
The other flow here, is the change of temperature over time; at least when the conditions are first imposed, starting from an equilibrium (say, cold) state. This involves heat capacity of the materials, and diffusibility and all that.
So that's probably part of the confusion.
Tim