Why a planet's atmosphere sets its cooling clock
A planet cools by radiating heat from its atmosphere into space. The composition and thickness of that atmosphere therefore control how quickly energy escapes. In the early atmospheres of ice giants, heavy elements such as water, ammonia, and methane can condense, and the latent heat released by that condensation keeps the atmosphere hot and the emission flux high for billions of years [1]. That does not slow cooling; it accelerates the loss of energy and shortens the cooling time compared with a planet whose atmosphere stays unchanged [1].
For low-mass planets, the situation is different. A gas envelope more massive than a few percent of the core can have a cooling time much longer than the time the planet takes to exit the protoplanetary disk, so the envelope cannot contract much before the disk disperses [3]. Once the disk is gone, stellar radiation drives a wind that strips the envelope, and the resulting mass loss drags internal heat outward. That makes the atmosphere cool and contract rapidly, until mass loss shuts down at about a tenth of the Bondi radius [3].
How long can a rocky planet stay hot after a giant impact?
For an Earth-sized planet struck by a Mars-sized body, the hot period can last more than a million years [4]. That figure comes from the immediate aftermath of a giant impact, when a large amount of energy is deposited in the planet. The million-year timescale is not a universal cooling time for all rocky planets; it is the duration of the hot phase following that specific kind of collision [4].
When does a planet's cooling time drop sharply?
The boil-off process can change the cooling time abruptly. As a low-mass planet loses its atmosphere, the cooling time-scale displays a sudden drop at the point of boil-off because the atmospheric mass decreases sharply [5]. Within a million years after the disk disperses, a planet may retain only about ten percent of its original envelope, and its Kelvin-Helmholtz time—the time it would take to cool by radiating its internal heat—becomes much longer than its actual age [3]. That means the planet is no longer cooling on its original schedule; it has lost most of the envelope that would have kept it warm.
Does large-scale volcanism control Earth's long-term cooling?
On million-year timescales, one proposed cooling mechanism is enhanced silicate weathering of freshly emplaced basalt from large igneous provinces. A study comparing the area of these provinces through the Phanerozoic with the extent of continental ice sheets found no significant correlation between total province area, or tropical province area, and ice sheet extent [2]. The largest peaks in tropical province area occur at times of non-glacial climate. These results suggest that changes in planetary weatherability from large igneous provinces are not the fundamental control on whether Earth is in a glacial or non-glacial state, although they could provide a secondary modulating effect alongside other processes [2].
Sources used in this answer
Acceleration of Cooling of Ice Giants by Condensation in Early Atmospheres
Latent heat release from condensing heavy elements in early ice-giant atmospheres keeps the atmosphere hot and emission high for billions of years, accelerating cooling and helping explain Uranus's low brightness.
Evaluating the Relationship Between the Area and Latitude of Large Igneous Provinces and Earth's Long‐Term Climate State
No significant correlation was found between large igneous province area (total or tropical) and continental ice sheet extent, suggesting that weathering changes from these provinces are not the fundamental control on Earth's glacial state.
Atmospheres of low-mass planets: the "boil-off"
Low-mass planets with envelopes more massive than a few percent of the core have cooling times longer than disk dispersal, but mass loss from a stellar-driven wind causes rapid cooling and contraction, leaving about ten percent of the envelope within a million years.
Emergence of a habitable planet
An Earth-sized planet struck by a Mars-sized impactor can remain hot for more than a million years.
Under the light of a new star: evolution of planetary atmospheres through protoplanetary disc dispersal and boil-off
The cooling time-scale of a planet shows a sudden drop at the point of boil-off due to the sharp decrease in atmospheric mass.