Observations of scattered light and thermal emission from hot Jupiter exoplanets have suggested the presence of inhomogeneous aerosols in their atmospheres. 3D general circulation models (GCMs) that attempt to model the effects of aerosols have been developed to understand the physical processes that underlie their dynamical structures. In this work, we investigate how different approaches to aerosol modeling in GCMs of hot Jupiters affect high-resolution thermal emission spectra throughout the duration of the planets orbit. Using results from a GCM with temperature-dependent cloud formation, we calculate spectra of a representative hot Jupiter with different assumptions regarding the vertical extent and thickness of clouds. We then compare these spectra to models in which clouds are absent or simply post-processed (i.e., added subsequently to the completed clear model). We show that the temperature-dependent treatment of clouds in the GCM produces high-resolution emission spectra that are markedly different from the clear and post-processed cases -- both in the continuum flux levels and line profiles -- and that increasing the vertical extent and thickness of clouds leads to bigger changes in these features. We evaluate the net Doppler shifts of the spectra induced by global winds and the planets rotation and show that they are strongly phase-dependent, especially for models with thicker and more extended clouds. This work further demonstrates the importance of radiative feedback in cloudy atmospheric models of hot Jupiters, as this can have a significant impact on interpreting spectroscopic observations of exoplanet atmospheres.