Why thermal paste is thin on purpose
Filling gaps without becoming a layer of its own.
Thermal paste is thin on purpose because its actual job is filling the microscopic gaps between two surfaces that look flat but are not, and any paste left thicker than that job strictly requires stops helping and starts acting as an extra insulating layer of its own, blocking exactly the heat flow it was applied to improve.
Flat surfaces touch at a few peaks
Two solid surfaces pressed together, however carefully machined, never touch across their whole area, because even a surface that looks and feels perfectly flat carries microscopic peaks and valleys. Where the peaks meet, real solid contact happens and heat conducts across easily. In the valleys between them a thin layer of air is trapped, and air conducts heat exceptionally poorly compared with almost any solid, so the true contact area between two pressed-together surfaces can be a small fraction of what it appears to be.
Thermal paste works by displacing that trapped air, flowing into the valleys and filling them with a material that conducts heat far better than air. Its usefulness comes entirely from replacing a poor conductor with a better one in a region that was going to exist regardless, making up for the contact that roughness prevents.
Clamping pressure plays a supporting part. Pressing the two surfaces together harder flattens the tallest peaks slightly, bringing more of them into contact and squeezing the valleys shallower, which is why a heatsink is bolted down firmly and evenly. Pressure alone can never close the valleys completely, though, and whatever remains of them is the space the paste is there to fill.
Better than air, worse than metal
Typical thermal paste conducts heat something like a hundred times better than still air, and roughly a hundred times worse than the copper of a heatsink base. Those two ratios explain the whole practice. Against the air it replaces in the valleys, paste is an enormous improvement. Against the metal on either side of it, every extra thickness of paste is a step down, so paste should sit only in the valleys and should add as little as possible to the distance between the two metal surfaces.
Too little paste leaves some of the valleys only partly filled, carrying heat little better than bare air, a patchy coverage that is often harder to spot afterwards than an obvious excess. Too much adds a layer of the worse conductor across the whole joint. Heat crossing a layer meets a resistance proportional to its thickness, so a smear 0.1 mm thick resists heat about four times as much as a film pressed down to 0.025 mm. A properly applied layer ends up thinner than a human hair, and seeing paste squeeze out around the edges of a joint once it is clamped is reassuring, evidence that the layer between the surfaces has been pressed down close to the thin film the gap called for.
Grease on a squeaking hinge
A squeaking door hinge responds well to a small dab of grease worked into the joint, enough to fill the microscopic gaps between the rubbing metal surfaces and let them move almost directly against each other with a thin, slippery film between. Slather the same hinge with a thick blob and the squeak may quiet down at first, but the hinge starts to feel sluggish and imprecise, because the excess grease has become a soft, separate layer holding the metal parts apart.
Thermal paste applied too thickly does the same thing in a different setting. A thin layer fills the valleys a machined surface cannot avoid and gets out of the way. A thick layer becomes its own material between the two real surfaces, and because paste conducts far worse than the metal on either side, the excess insulates. Both mistakes come from the same instinct, reasoning that if a little of a material clearly helps, a lot must help more. The material's usefulness was always tied to the gap it was filling, and a hinge or a heatsink has only so much gap to fill.
Repeated heating and cooling can work paste out of a joint over years of service, a slow migration engineers call pump-out, in which each cycle's expansion and contraction squeezes a little more of the softened paste toward the edges until the centre, doing most of the real work, runs thinner than it was meant to and begins to open up small dry patches of its own.
Applying it and reapplying it
Instructions for applying thermal paste consistently say to use less, spreading a thin, even film or a small central dot that mounting pressure will spread, because paste beyond what the microscopic gap needs adds thickness that measurably worsens heat transfer. Past a certain point the paste stops filling a gap and starts being the gap, insulating exactly where the whole point was to conduct. Two surfaces clamped tightly together with a thin film between them, squeezed out until it is barely visible at the edges, will run cooler than the same two surfaces separated by a generous, confident-looking smear.
The same reasoning explains why reusing old, dried paste after taking a joint apart rarely works as well as applying a fresh layer. Paste that has already hardened, or been squeezed down to its minimum thickness once, cannot simply be pressed thinner a second time, and when the parts go back together its old ridges and hollows rarely line up again with the peaks and valleys of the metal. Cleaning both surfaces back to bare metal and starting again with a small amount of fresh paste restores the thin, gap-filling film the joint was designed around.