  A search for a heavy resonance decaying into a top quark and a W boson in
proton-proton collisions at $\sqrt{s} =$ 13 TeV is presented. The data analyzed
were recorded with the CMS detector at the LHC and correspond to an integrated
luminosity of 138 fb$^{-1}$. The top quark is reconstructed as a single jet and
the W boson, from its decay into an electron or muon and the corresponding
neutrino. A top quark tagging technique based on jet clustering with a variable
distance parameter and simultaneous jet grooming is used to identify jets from
the collimated top quark decay. The results are interpreted in the context of
two benchmark models, where the heavy resonance is either an excited bottom
quark b$^*$ or a vector-like quark B. A statistical combination with an earlier
search by the CMS Collaboration in the all-hadronic final state is performed to
place upper cross section limits on these two models. The new analysis extends
the lower range of resonance mass probed from 1.4 down to 0.7 TeV. For
left-handed, right-handed, and vector-like couplings, b$^*$ masses up to 3.0,
3.0, and 3.2 TeV are excluded at 95% confidence level, respectively. The
observed upper limits represent the most stringent constraints on the b$^*$
model to date.
