Despite the great observational success of the standard cosmological model some discrepancies in the inferred parameter constraints have manifested among a number of cosmological data sets. These include a tension between the expansion rate of our Cosmos as inferred from the cosmic microwave background (CMB) and as found from local measurements, the preference for an enhanced amplitude of CMB lensing, a somewhat low quadrupole moment of the CMB fluctuations as well as a preference for a lower amplitude of matter fluctuations in large-scale structure surveys than inferred from the CMB. We analyse these observational tensions under the addition of spatial curvature and a free CMB background temperature that may deviate from its locally measured value. With inclusion of these parameters, we observe a trend in the parameter constraints from CMB and baryon acoustic oscillation data towards an open and hotter universe with larger current expansion rate, standard CMB lensing amplitudes, lower amplitude of matter fluctuations, and marginally lower CMB quadrupole moment, consistently reducing the individual tensions among the cosmological data sets. Combining this data with local distance measurements, we find a preference for an open and hotter universe beyond the 99.7% confidence level. Finally, we briefly discuss a local void as a possible source for a deviation of the locally measured CMB temperature from its background value and as mimic of negative spatial curvature for CMB photons. This interpretation implies a $sim$20% underdensity in our local neighbourhood of $sim$10-100 Mpc in diameter, which is well within cosmic variance.
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