  Thermal pure state algorithms, which employ pure quantum states representing
thermal equilibrium states instead of statistical ensembles, are useful both
for numerical simulations and for theoretical analysis of thermal states.
However, their inherently large entanglement makes it difficult to represent
efficiently and limits their use in analyzing large systems. Here, we propose a
new algorithm for constructing thermal pure states for systems with certain
antiunitary symmetries, such as time-reversal or complex conjugation symmetry.
Our method utilizes thermal pure states that, while exhibiting volume-law
entanglement, can be mapped to tensor network states through simple
transformations. Furthermore, our approach does not rely on random sampling and
thus avoids statistical uncertainty. Moreover, we can compute not only thermal
expectation values of local observables but also thermodynamic functions. We
demonstrate the validity and utility of our method by applying it to the
one-dimensional XY model and the two-dimensional Ising model on a triangular
lattice. Our results suggest a new class of variational wave functions for
volume-law states that are not limited to thermal equilibrium states.
