Neuromorphic systems that employ advanced synaptic learning rules, such as the three-factor learning rule, require synaptic devices of increased complexity. Herein, a novel neoHebbian artificial synapse utilizing ReRAM devices has been proposed and experimentally validated to meet this demand. This synapse features two distinct state variables: a neuron coupling weight and an "eligibility trace" that dictates synaptic weight updates. The coupling weight is encoded in the ReRAM conductance, while the "eligibility trace" is encoded in the local temperature of the ReRAM and is modulated by applying voltage pulses to a physically co-located resistive heating element. The utility of the proposed synapse has been investigated using two representative tasks: first, temporal signal classification using Recurrent Spiking Neural Networks (RSNNs) employing the e-prop algorithm, and second, Reinforcement Learning (RL) for path planning tasks in feedforward networks using a modified version of the same learning rule. System-level simulations, accounting for various device and system-level non-idealities, confirm that these synapses offer a robust solution for the fast, compact, and energy-efficient implementation of advanced learning rules in neuromorphic hardware.