Design research faces a critical 'impact gap' where the potential for scientific and practical impact is yet to be fully realised. A key means of bridging this gap is the adoption of fundamental theory from other fields to support clarification and synergy in design research. In this paper we examine one of the main candidates for adoption: dual-process theory of cognition. Cognition forms a common element across much of the design literature and leads to fundamental dual-process theories of reasoning. While dual-process theory has started to be recognised in design research, its widespread recognition and potential utility have not been widely explored. Following a conceptual theory development approach we identify and logically describe interactions between dual-process theory and design research. We conclude the paper with a proposition of a design research framework with a core rooted in dual-process theory, and based on this, an agenda for theory-driven design research. This contributes to the debate on how to improve impact, and theoretical and scientific rigour in design research, and provides a concrete agenda for discussion and development within the community.