= Solution
Let the stellar radius and temperature be $R_*$ and $T_*$. Assume <Bond albedo> $A_B$, isotropic stellar emission, blackbody planetary emission, and complete redistribution over the tidally locked planet. The absorbed stellar power is
$$
P_{\rm abs}=\pi R_p^2(1-A_B)\sigma T_*^4
\left(\frac{R_*}{a}\right)^2.
$$
Adding the isolated internal luminosity $4\pi R_p^2\sigma T_0^4$ and balancing the total against $4\pi R_p^2\sigma T_{\rm eq}^4$ gives the <planetary equilibrium temperature>
$$
\boxed{T_{\rm eq}^4=T_0^4
+(1-A_B)T_*^4\frac{R_*^2}{4a^2}}.
$$
If heat is reradiated uniformly only over the dayside, replace the denominator $4a^2$ by $2a^2$. The latter is often more plausible for inefficient redistribution on a tidally locked bare planet.
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