We investigate the thermodynamical properties of strange quark matter (SQM) at zero/finite temperature and under constant magnetic field within quasiparticle model. The quark matter symmetry energy, energy per baryon, free energy per baryon, anisotropic pressures are also studied and the result indicates that both the effects of temperature and magnetic field can significantly influence the thermodynamical properties of quark matter and proto-quark stars (PQSs). Our result also indicates that the maximum mass and the core temperature of PQSs not only depends on the heating process at the isentropic stages, but also but also the magnetic field strength and orientation distribution inside the magnetar within quasiparticle model.