13.8 | How long until the Universe cools by 0.1 K?

Assume the Universe has present density parameter $\Omega_0=1$, no dark energy, and present temperature $T_i=2.73\,\mathrm K$. Its temperature is inversely proportional to its scale factor. How long, starting now, will it take to cool by $0.1\,\mathrm K$?

Express the answer in terms of the present Hubble parameter $H_i$. For numerical values, use $H_i^{-1}\approx13.7\times10^9$ years (about $71.4\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$); the original statement does not specify this constant.