We consider the problem of parameter estimation for inhomogeneous cluster point processes in the space-time setting, with the aim to avoid the usual assumption of the space-time separability of the first-order intensity function. We focus on the class of second-order intensity reweighted shot-noise Cox processes and take advantage of the minimum contrast estimation based on the space-time K-function K(r,t) as a function of two arguments: the spatial distance r and the temporal lag t. We discuss the estimation using the whole surface of K(r,t) and also the possibility to simplify the optimization procedure by considering only some profiles of this surface.

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