Interpersonal physiological entrainment is increasingly argued to underlie rapport, empathy and even team performance. Inspired by the model of interpersonal synergy, we investigate the presence, temporal development, possible mechanisms and impact of interpersonal heart rate entrainment during individual and collective creative LEGO construction tasks. In Study 1 we show how HR entrainment is driven by a plurality of sources including task constraints and behavioral coordination. Generally, HR entrainment is more prevalent in individual trials (involving participants doing the same things) than in collective ones (involving participants taking turns and performing complementary actions). However, when contrasted against virtual pairs, collective trials display more stable HR entrainment supporting the idea that online social interaction plays a role. Furthermore, HR entrainment is found to grow across collective but not individual trials. In Study 2 we further show that in collective trials the dynamics of HR entrainment is statistically predicted by interpersonal speech and building coordination. In Study 3, we explore the relation between HR entrainment, behavioral coordination, and rapport and perceived group competence. While behavioral coordination predicts rapport and group competence, HR entrainment does not. Physiological entrainment, thus, should not be considered a universal unmediated proxy for shared emotions, empathy and collective performance, but should be considered within the constraints and functional demands of the ongoing activity. Behavioral coordination - at least in tasks requiring forms of joint action - seems to be more informative of both physiological entrainment and collective experience.