  We analyze several spherically symmetric exterior vacuum solutions allowed by
the Einstein-Aether (EA) theory with a non static aether and study the
thermodynamics of their Killing and universal horizons. We show that there are
five classes of solutions corresponding to different values of a combination of
the free parameters, $c_{2}$, $c_{13}=c_1+c_3$ and $c_{14}=c_1+c_4$, which are:
(A) $c_2 \ne 0$ and $c_{13} \ne 0$ and $c_{14}=0$, (B) $c_2 \ne 0$ and $c_{13}
= 0$ and $c_{14} = 0$, (C) $c_2 = 0$ and $c_{13} \ne 0$ and $c_{14} = 0$, (D)
$c_2 = 0$, $c_{13} = 0$ and $c_{14} \ne 0$, and (E) $c_2 = - c_{13} \ne 0$ and
$c_{14} \ne 0$. We present explicit analytical solutions for these five cases.
All these cases have singularities at $r=0$ and are asymptotically flat
spacetimes and possess both Killing and universal horizons with the universal
horizons always being inside the Killing horizons. Finally, we compute the
surface gravity, the temperature, the entropy and the first law of
thermodynamics for the universal horizons.
