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With a temperature akin to an M-dwarf, WASP-33b is among the hottest Jupiters known, making it an ideal target for high-resolution optical spectroscopy. By analyzing both transmission and emission spectra, we aim to substantiate previous reports of atmospheric TiO and a thermal inversion within the planet's atmosphere. We observed two transits and six arcs of the phase curve with ESPaDOns on the Canada-France-Hawaii Telescope and HIRES on the Keck telescope, which provide high spectral resolution and ample wavelength coverage. We employ the Doppler cross-correlation technique to search for the molecular signatures of TiO and H$_2$O in these spectra, using models based on the TiO line list of Plez (2012). Though we cannot exclude line-list-dependent effects, our data do not corroborate previous indications of a thermal inversion. Instead we place a $3σ$ upper limit of $10^{-9}$ on the volume mixing ratio of TiO for the T-P profile we consider. While we are unable to constrain the volume mixing ratio of water, our strongest constraint on TiO comes from day-side emission spectra. This apparent absence of a stratosphere sits in stark contrast to previous observations of WASP-33b as well as theoretical predictions for the atmospheres of highly irradiated planets. The discrepancy could be due to variances between line lists, and we stress that detection limits are only as good as the line list employed, and are only valid for the specific T-P profile considered due to the strong degeneracy between lapse rate ($dT/d\log P$) and molecular abundance.