Proofs as epistemic tools are central to mathematical practice, as they establish and provide explanations for the validity of mathematical statements. Considering the challenge that proof construction poses to learners of all ages, prior research has investigated its cognitive determinants, but the impact of affective-motivational experiences on proof construction has been insufficiently investigated. Emotions related to knowledge acquisition (i.e., epistemic emotions) are assumed to play a key role in epistemic processes. In this study we investigated how the performance of 80 mathematics undergraduate students in a geometric proof construction task relates to the epistemic emotions experienced during proof construction. Controlling for geometry knowledge, we included control and value appraisals as antecedents in our investigation of epistemic emotions, and attention and motivation as mediators of their effects on proof construction performance. The results indicate that positive as well as negative emotions are influenced by students' appraisals, also indicating an interaction of both appraisal dimensions. Primarily enjoyment and curiosity mediate the effects of these appraisals on attention and motivation. These two markers of the proof construction process, in turn, mediate the effects of enjoyment and boredom on proof construction performance. In this study we investigated systematically the role of epistemic emotions in geometric proof construction and we offer insights that complement the existing research on the cognitive determinants of proof performance. Moreover, this study extended research on epistemic emotions into the area of proof construction, an epistemic process central to mathematics.