  The tensor renormalization group is a promising numerical method used to
study lattice statistical field theories. However, this approach is
computationally expensive in 2+1 and 3+1 dimensions. Here we use tensor
renormalization group methods to study an effective three-dimensional
$\mathbb{Z}_{3}$ model for the heavy-quark, high-temperature, strong-coupling
limit of single-flavor 3+1 dimensional quantum chromodynamics. Our results are
cross-checked using the worm Monte Carlo algorithm. We present the phase
diagram of the model through the measurement of the Polyakov loop, the
nearest-neighbor Polyakov loop correlator, and their susceptibilities. The
tensor renormalization group results are in good agreement with the literature
