Evidence for the former presence of ground ice and its possible role in the erosion of Valles Marineris trough walls is equivocal. This study aims to determine whether variations in the topographic slope angle of the walls of the trough Coprates Chasma are consistent with predicted temperature-driven differences in the distribution, thermal condition, and strength of ground ice within its walls. Using Mars Orbiter Laser Altimeter topographic data, 247 profiles were made rim to rim across the trough and measurements made of wall slope angle, mean annual surface temperature, and trough geometry (wall height, rim elevation, and trough width). Variations in these parameters along each trough wall, and differences between the two trough walls, were established. The results indicate that the predicted variations along and differences between the walls in the three-dimensional distribution of ground ice, and in its thermal condition and strength, are unlikely to have caused the measured variations in trough wall slope angle. These observations imply that ground ice has been absent within the trough walls since the age of formation of the spur-and-gully wall morphology. The results preclude the spur-and-gully morphology having developed by dry mass-wasting of material above an ice-rich cryosphere and indicate the action of liquid water to be a more likely origin. The inferred absence of ice within the walls precludes any role of ice in initiating or mobilizing landslides where they have eroded the spur-and-gully morphology.