A tissue snare comprises an elongated member having a distal end and a loop formed of a shape memory material, the loop including a tissue receiving interior opening and being connected to the distal end of the elongated member, properties of the shape memory material being selected so that, when a temperature of the loop exceeds a critical temperature thereof, the loop constricts from an expanded state to a constricted state. A method of treating tissue comprises placing a loop of a snare around a portion of tissue to be treated while the loop is in an expanded configuration, the loop being formed of a shape memory material having a critical temperature so that, when a temperature of the loop is above the critical temperature, the loop transitions from the expanded configuration to a constricted configuration in combination with transitioning, after the loop has been placed around the portion of tissue to be treated, the loop from the expanded configuration to the constricted configuration to tighten the loop around the portion of tissue to be treated.
