  In the present universe, magnetic fields exist with various strengths and on
various scales. One possible origin of these cosmic magnetic fields is the
primordial magnetic fields (PMFs) generated in the early universe. PMFs are
considered to contribute to matter density evolution via Lorentz force and the
thermal history of intergalactic medium (IGM) gas due to ambipolar diffusion.
Therefore, information about PMFs should be included in the temperature
anisotropy of the Cosmic Microwave Background through the thermal
Sunyaev-Zel'dovich (tSZ) effect in IGM. In this article, given an initial power
spectrum of PMFs, we show the spatial fluctuation of mass density and
temperature of the IGM and tSZ angular power spectrum created by the PMFs.
Finally, we find that the tSZ angular power spectrum induced by PMFs becomes
significant on small scales, even with PMFs below the observational upper
limit. Therefore, we conclude that the measurement of tSZ anisotropy on small
scales will provide the most stringent constraint on PMFs.
