Humanistic research fields such as media archaeology, critical posthumanism, and the environmental humanities, have recently directed attention to the notion of deep time as a perspective providing new analytical and ethical traction on both temporalities and materialities of media technologies. In essence, deep time is concerned with long-term geological processes, taking into account material developments and impacts over long periods of time. Synthesizing insights from HCI research on temporality, materiality, and sustainability with understandings from humanistic deep time research, this paper is a first attempt at articulating the potential of deep time design thinking in HCI. The paper presents three practical ‘sensibilities’ that help designers and HCI researchers to address new classes and timescales of wicked problems.