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Heat flow is an important constraint on planetary formation and evolution. Ithas been suggested that Martian obliquity cycles might cause periodic collapsesin atmospheric pressure, leading to corresponding decreases in regolith thermalconductivity (which is controlled by gas in the pore spaces). Geothermal heatwould then build up in the subsurface, potentially affecting present-day heatflow - and thus the measurements made by a heat-flow probe such as the InSightHP$^{3}$ instrument. To gauge the order of magnitude of this effect, we modelthe diffusion of a putative heat pulse caused by thermal conductivity changeswith a simple numerical scheme and compare it to the heat-flow perturbationscaused by other effects. We find that an atmospheric collapse to 300 Pa in thelast 40 kyr would lead to a present-day heat flow that is up to $2-8\%$ largerthan the average geothermal background. Considering the InSight mission withexpected $5-15\%$ error bars on the HP$^{3}$ measurement, this perturbationwould only be significant in the best-case scenario of full instrumentdeployment, completed measurement campaign, and a well-modelled surfaceconfiguration. The prospects for detecting long-term climate perturbations viaspacecraft heat-flow experiments remain challenging.

Potential Effects of Atmospheric Collapse on Martian Heat Flow and Application to the InSight Measurements