  We examine the accuracy of the microcanonical Lanczos method (MCLM) developed
by Long, {\it et al.} [Phys. Rev. B {\bf 68}, 235106 (2003)] to compute
dynamical spectral functions of interacting quantum models at finite
temperatures. The MCLM is based on the microcanonical ensemble, which becomes
exact in the thermodynamic limit. To apply the microcanonical ensemble at a
fixed temperature, one has to find energy eigenstates with the energy
eigenvalue corresponding to the internal energy in the canonical ensemble.
Here, we propose to use thermal pure quantum state methods by Sugiura and
Shimizu [Phys. Rev. Lett. {\bf 111}, 010401 (2013)] to obtain the internal
energy. After obtaining the energy eigenstates using the Lanczos
diagonalization method, dynamical quantities are computed via a continued
fraction expansion, a standard procedure for Lanczos-based numerical methods.
Using one-dimensional antiferromagnetic Heisenberg chains with $S=1/2$, we
demonstrate that the proposed procedure is reasonably accurate even for
relatively small systems.
