For large scale distributed systems, designing energy efficient protocols and services has become as significant as considering conventional performance criteria like scalability, reliability, fault-tolerance and security. We consider frequent item set discovery problem in this context. Although it has attracted attention due to its extensive applicability in diverse areas, there is no prior work on energy cost model for such distributed protocols. In this paper, we develop an energy cost model for frequent item set discovery in unstructured P2P networks. To the best of our knowledge, this is the first study that proposes an energy cost model for a generic peer using gossip-based communication. As a case study protocol, we use our gossip-based approach ProFID for frequent item set discovery. After developing the energy cost model, we examine the effect of protocol parameters on energy consumption using our simulation model on PeerSim and compare push-pull method of ProFID with the well-known push-based gossiping approach. Based on the analysis results, we reformulate the upper bound for the peer's energy cost.