Mediated social touch technologies aim to transmit the sense of touch between two or more physically distributed partners. Previous work in CSCW has focused mostly on vibrotactile actuation, though there is also significant recent interest in exploring a wider variety of haptic actuation modalities. In this paper, we explore Shape Memory Alloys as a novel means for constriction and heat activation. We demonstrate the feasibility of this approach by implementing the SqueezeBands system, which augments social gestures over videochat with haptic actuation. We describe an evaluation of the system with 57 pairs of participants, collaborating on tasks either high or low emotional salience. Our results demonstrate that SqueezeBands encourage greater and more diverse demonstrations of touch and that they may be particularly appropriate for easing mental and physical demand in high emotion tasks. We end with a discussion of the opportunities and challenges in leveraging Shape Memory Alloy actuation for mediated social touch.