There is to date little research on the pedagogy of entrepreneurship and innovation aligned with sustainability. This study makes a case for, and empirically investigates, the value of a pedagogical approach to sustainable entrepreneurship and innovation that is intended to be transformative of participants. Following Sipos et al. (2008), we propose that such an approach should address all three pedagogical dimensions of abstract knowledge (head), practical competences (hands), and motivation (affect or heart). We take as an empirical probe the training offered by the European Institute of Innovation & Technology (EIT) Climate-KIC graduate education programme, a European Commission-funded initiative to develop sustainability-oriented technology entrepreneurs and innovators. Repertory grid-based interviews are undertaken with two cohorts of students, investigating the proposition that transformative, multidimensional approaches are appropriate for sustainable entrepreneurship education. We are presenting here an insider view of an EIT learning journey, a ‘lived experience’ view of how addressing all three pedagogical dimensions - Head, Hands and Heart – support transformative education in a sustainable entrepreneurship context. We argue that EIT training does offer all three educational elements and that these are viewed as valuable and transformative and that the affective dimension of learning had a strong impact on the participants. We observe that the concept of sustainable entrepreneurship seems to raise more cognitive and normative tensions than the concept of sustainable innovation, perhaps through the association of entrepreneurship with the profit motive.