  Coupled cluster (CC) has established itself as a powerful theory to study
correlated quantum many-body systems. Finite-temperature generalizations of CC
theory have attracted considerable interest and have been shown to work as
nicely as the ground-state theory. However, most of these recent developments
address only fermionic or bosonic systems. The distinct structure of the
$su(2)$ algebra requires the development of a similar thermal CC theory for
spin degrees of freedom. In this paper, we provide a formulation of our
thermofield-inspired thermal CC for SU(2) systems. We apply the thermal CC to
the Lipkin-Meshkov-Glick system as well as the one-dimensional transverse field
Ising model as benchmark applications to highlight the accuracy of thermal CC
in the study of finite-temperature phase diagrams in SU(2) systems.
