Mercury's large core generates a magnetic field and harbors a solidified inner component. These features constrain models of the planet's thermal history. The mantle provides the boundary condition on Mercury's core that determines heat loss. Recent studies suggest Mercury's mantle may have a higher thermal diffusivity than the silicate shells of other rocky bodies due to iron depletion. Considering the role of diffusivity, we model Mercury's mantle starting from a post magma-ocean state by calculating core-mantle boundary heat flow and the ratio of inner-core boundary radius to core-mantle boundary radius, $f_c$, for periods comparable to the age of the solar system. Core-mantle boundary (CMB) heat flow is calculated using 3D mantle convection simulations for thermal diffusivities, κ, ranging from 1.0 - 3.0 $\times {10}^{-6}$ m²/s and initial radiogenic uniform mantle heating rates, χ, of 0 - 40 pW/kg (that decay with a 3 Gyr half-life). Several scenarios can unfold for the range of parameters considered: these include cases featuring both the cessation of mantle convection and its continuation at 4.5 Gyr. We map a trend in κ - χ space and find that for some parameters present-day core heat flux and inner-core size estimates are satisfied for a Mercurian mantle that is cooling by conduction. The influence of initial sulfur fraction in the core was examined for a subset of cases. For a sulfur fraction of 0.10, $f_c$ falls between 0.1 and 0.55 which corresponds to planetary radius contractions below 7 km (since the Late Heavy Bombardment). However, $f_c$ exceeds 0.55 for a lower initial sulfur fraction and results in planetary contraction in excess of 7 km. In general, we find that the mean core heat flux reaches a temporal local minimum when the mantle transitions from a convective to a conductive regime and subsequently climbs before decreasing. The transition to conduction is delayed with increased mantle internal heating rate but the maximum mean heat flux from the core into the conducting and cooling mantle is always greater than the heat flux observed at the cessation of the stagnant-lid convection. We find that for an initially more vigorously convecting mantle the onset of inner-core growth is earlier while the basal heat flux is marginally reduced at present day. In general, we find that current-day conductive cooling of the Mercurian mantle can satisfy estimates on Mercury's core heat loss inferred from the strength of its magnetic field while also satisfying the limits on the present-day size of its inner core.

水星的大核产生磁场并含有凝固的内部成分。这些特征限制了行星热历史的模型。地幔为水星核心提供了决定热损失的边界条件。最近的研究表明，由于铁耗竭，水星的地幔可能比其他岩石天体的硅酸盐壳具有更高的热扩散率。考虑到扩散率的作用，我们通过计算核-幔边界热流和核内边界半径与核-幔边界半径的比值来模拟从后岩浆-海洋状态开始的水星地幔，$F_C$，对于与太阳系年龄相当的时期。核-地幔边界 (CMB) 热流使用 3D 地幔对流模拟计算，热扩散系数κ范围为 1.0 - 3.0$\times {10}^{-6}$m ² /s 和初始放射成因均匀地幔加热速率χ为 0 - 40 pW/kg（衰减半衰期为 3 Gyr）。对于所考虑的参数范围，可以展开几种情况：这些情况包括地幔对流停止及其在 4.5 Gyr 继续进行的情况。我们绘制了κ - χ空间的趋势图，并发现对于通过传导冷却的水星地幔，对于某些参数，当前的核心热通量和内核尺寸估计值是令人满意的。针对部分情况检查了岩心中初始硫含量的影响。对于 0.10 的硫分数，$F_C$介于 0.1 和 0.55 之间，这对应于低于 7 公里的行星半径收缩（自晚期重轰炸）。然而，$F_C$对于较低的初始硫含量超过 0.55 并导致行星收缩超过 7 公里。一般而言，我们发现当地幔从对流状态转变为传导状态并随后在下降之前上升时，平均核心热通量达到时间局部最小值。随着地幔内部加热速率的增加，向传导的转变被延迟，但从核心进入传导和冷却地幔的最大平均热通量总是大于在停滞盖对流停止时观察到的热通量。我们发现，对于最初对流更强烈的地幔，内核增长的开始较早，而基础热通量目前略有减少。总的来说，我们发现目前水星地幔的传导冷却可以满足对水星的估计。