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We present new functionality within PICASO, a state-of-the-art radiative transfer model for exoplanet and brown dwarf atmospheres, by developing a new pipeline that computes phase-resolved thermal emission (thermal phase curves) from three-dimensional (3D) models. Because PICASO is coupled to Virga, an open-source cloud code, we are able to produce cloudy phase curves with different sedimentation efficiencies ($f_{sed}$) and cloud condensate species. We present the first application of this new algorithm to hot Jupiter WASP-43b. Previous studies of the thermal emission of WASP-43b from Kataria et al. found good agreement between cloud-free models and dayside thermal emission, but an overestimation of the nightside flux, for which clouds have been suggested as a possible explanation. We use the temperature and vertical wind structure from the cloud-free 3D general circulation models of Kataria et al. and post-process it using PICASO, assuming that clouds form and affect the spectra. We compare our models to results from Kataria et al., including Hubble Space Telescope Wide-Field Camera 3 (WFC3) observations of WASP-43b from Stevenson et al. In addition, we compute phase curves for Spitzer at 3.6 and 4.5 $μm$ and compare them to observations from Stevenson et al. We are able to closely recover the cloud-free results, even though PICASO utilizes a coarse spatial grid. We find that cloudy phase curves provide much better agreement with the WFC3 and Spitzer nightside data, while still closely matching the dayside emission. This work provides the community with a convenient, user-friendly tool to interpret phase-resolved observations of exoplanet atmospheres using 3D models.