This article considers the problem of throughput maximization for a hybrid energy harvesting and simultaneous wireless information and power transfer (EH-SWIPT) relay system subject to energy/temperature constraints at the transmitting/receiving nodes. An EH-based single antenna source sends information to a single-antenna destination via a cooperative half-duplex multi-antenna relay, wherein the relay applies power splitting (PS) technique for obtaining energy to forward information to the destination. It is also assumed that, the receiving nodes are subject to a peak temperature constraint. Two transmission scenarios are considered; Single time slot, and multiple ones. For both scenarios, achievable rate/throughput of the system is derived and optimal resource allocations, i.e. transmission powers of the source and the relay and the optimal PS ratios at the relay, are obtained. First the multiple time slots scenario is presented, and non-convexity of the optimization problem is tackled by proposing an iterative algorithm based on closed form expressions. Then, for the single time slot one, globally optimal resource allocations are obtained. For both scenarios, some special cases are considered to better reflect the performance characteristics of the system. Finally, numerical results are presented to highlight the effect of optimal resource allocation on system performance.