  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.
