The importance of the thermal characteristics of subglacial deformable debris is inferred from effects on processes of deposition and erosion. There is a lack of information on the temperatures found within subglacial debris under present-day ice masses. Data on the thermal conditions beneath Quaternary ice sheets, especially in the marginal areas where deformable material existed, must be obtained so that land-forming processes and the sedimentary environment beneath glaciers can be better understood. Four models illustrate, theoretically, the possible influences oscillating freezing fronts may have on subglacial debris. These models reveal that, depending upon the nature of the substructure, both erosion and deposition may occur under differing conditions and also that a “surge-type” condition may be created.