We propose a novel method to constrain the Milky Way (MW) mass $M_{rm vir}$ with its corona temperature observations. For a given corona density profile, one can derive its temperature distribution assuming a generalized equilibrium model with non-thermal pressure support. While the derived temperature profile decreases substantially with radius, the X-ray-emission-weighted average temperature, which depends most sensitively on $M_{rm vir}$, is quite uniform toward different sight lines, consistent with X-ray observations. For an Navarro-Frenk-White (NFW) total matter distribution, the corona density profile should be cored, and we constrain $M_{rm vir}=(1.19$ - $2.95) times 10^{12} M_{rm sun}$. For a total matter distribution contributed by an NFW dark matter profile and central baryons, the corona density profile should be cuspy and $M_{rm vir,dm}=(1.34$ - $5.44) times 10^{12} M_{rm sun}$. Non-thermal pressure support leads to even higher values of $M_{rm vir}$, while a lower MW mass may be possible if the corona is accelerating outward. This method is independent of the total corona mass, its metallicity, and temperature at very large radii.
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