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We observed Ceres at three epochs in 2015 November and 2017 September and October with ALMA 12-meter array and in 2017 October with the ALMA Compact Array (ACA), all at ~265 GHz continuum (wavelengths of ~1.1 mm) to map the temperatures of Ceres over a full rotation at each epoch. We also used 2017 October ACA observations to search for HCN. The disk-averaged brightness temperature of Ceres is measured to be between 170 K and 180 K during our 2017 observations. The rotational lightcurve of Ceres shows a double peaked shape with an amplitude of about 4%. Our HCN search returns a negative result with an upper limit production rate of ~2$\times$10$^{24}$ molecules s$^{-1}$, assuming globally uniform production and a Haser model. A thermophysical model suggests that Ceres's top layer has higher dielectric absorption than lunar-like materials at a wavelength of 1 mm. However, previous observations showed that the dielectric absorption of Ceres decreases towards longer wavelengths. Such distinct dielectric properties might be related to the hydrated phyllosilicate composition of Ceres and possibly abundant $μ$m-sized grains on its surface. The thermal inertia of Ceres is constrained by our modeling as likely being between 40 and 160 tiu, much higher than previous measurements at infrared wavelengths. Modeling also suggests that Ceres's lightcurve is likely dominated by spatial variations in its physical or compositional properties that cause changes in Ceres's observed thermal properties and dielectric absorption as it rotates.