The \emph{temporal multi-dimensional join} (TMDJ) is a simple parameterizable operator which offers a systematic and efficient implementation for a wide range of advanced temporal operators. We start out by formalizing point-based, interval-based and duplicate-aware temporal operators. These are crucial but often confused semantic properties of temporal operators. We show that these semantic properties can be determined via a parameterization of the TMDJ. Finally, we describe a lightweight implementation of the TMDJ and report experimental results which show the performance of advanced temporal operations is orders of magnitude better than the performance of equivalent SQL solutions.