Present-day temperature $T_0$ of cosmic microwave background has been precisely measured by the FIRAS experiment. We identify that the early dark energy (EDE) (non-negligible around matter-radiation equality) scenario can remain compatible with the FIRAS result, while lifting the Hubble constant $H_0$. We perform Monte Carlo Markov chain analysis to confirm our observations. We also present an $alpha$-attractor Anti-de Sitter (AdS) model of EDE, in which the AdS depth is consistently varied in the Monte Carlo Markov chain analysis. We found that our datasets weakly hinted the existence of an AdS phase near recombination with $H_0sim 73$km/s/Mpc at 1$sigma$ region in the best-fit model.
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