  We investigate finite-temperature observables in three-dimensional large $N$
critical vector models taking into account the effects suppressed by $1\over
N$. Such subleading contributions are captured by the fluctuations of the
Hubbard-Stratonovich auxiliary field which need to be handled with care due to
a subtle divergence structure which we clarify. The examples we consider
include the scalar $O(N)$ model, the Gross-Neveu model, the Nambu-Jona-Lasinio
model and the massless Chern-Simons Quantum Electrodynamics. We present
explicit results for the free energy density to the subleading order in $1\over
N$, which captures the thermal one-point function of the stress-energy tensor
to this order. We also include the dependence on a chemical potential. We
determine the Wilson coefficient in the thermal effective action that is
sensitive to global symmetry for the first time directly in interacting CFTs,
which produces a symmetry-resolved asymptotic density of states. We further
provide a formula from diagrammatics for the one-point functions of general
single-trace higher-spin currents. We observe that in most cases considered,
these subleading effects lift the apparent degeneracies between observables in
different models at infinite $N$, while in special cases the discrepancies only
start to appear at the next-to-subleading order.
