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We present a novel approach to improve temporal coherence in Monte Carlo renderings of animation sequences. Unlike other approaches that exploit temporal coherence in a post-process, our technique does so already during sampling. Building on previous gradient-domain rendering techniques that sample finite differences over the image plane, we introduce temporal finite differences and formulate a corresponding 3D spatio-temporal screened Poisson reconstruction problem that is solved over windowed batches of several frames simultaneously. We further extend our approach to include second order, mixed spatio-temporal differences, an improved technique to compute temporal differences exploiting motion vectors, and adaptive sampling. Our algorithm can be built on a gradient-domain path tracer without large modifications. In particular, we do not require the ability to evaluate animation paths over multiple frames. We demonstrate that our approach effectively reduces temporal flickering in animation sequences, significantly improving the visual quality compared to both path tracing and gradient-domain rendering of individual frames.