While current medium access control solutions in low-power wide area networks are generally based on Aloha, recent studies demonstrated the interest of adding carrier sense mechanisms to the picture. In this paper, we investigate the impact of the carrier sense threshold parameter in this particular context. We show that its impact on the average behavior of the network is limited, but this changes when looking at the individual node performance. Our simulation results demonstrate an important heterogeneity among nodes, both in terms of packet success probability and of energy consumption. Moreover, the performance of the nodes is strongly correlated with the percentage of contending nodes that they can sense. By simply using two different carrier sense thresholds in the network, we achieve an increased fairness among nodes.