Machine-to-Machine (M2M) networks are an emerging technology with applications in various fields, including smart grids, healthcare, vehicular telematics and smart cities. Heterogeneous M2M networks contain different types of nodes, e.g., nodes that send emergency, periodic, and normal type data. An important problem is to rapidly estimate the number of active nodes of each node type in every time frame in such a network. In this paper, we design two schemes for estimating the active node cardinalities of each node type in a heterogeneous M2M network with $T$ types of nodes, where $T \ge 2$ is an arbitrary integer. Our schemes consist of two phases-- in phase 1, coarse estimates are computed, and in phase 2, these estimates are used to compute the final estimates to the required accuracy. We analytically derive a condition for one of our schemes that can be used to decide as to which of two possible approaches should be used in phase 2 to minimize its execution time. The expected number of time slots required to execute and the expected energy consumption of each active node under one of our schemes are analysed. Using simulations, we show that our proposed schemes require significantly fewer time slots to execute compared to estimation schemes designed for a heterogeneous M2M network in prior work, and also, compared to separately executing a well-known estimation protocol designed for a homogeneous network in prior work $T$ times to estimate the cardinalities of the $T$ node types, even though all these schemes obtain estimates with the same accuracy.