Transmission of a normally incident plane wave through a metasurface with bicontrollable subwavelength scattering elements was simulated using a commercial software. Some pixels composing the H-shaped scattering elements were made of a magnetostatically controllable material whereas the remaining pixels were made of a thermally controllable material, the metasurface designed to operate in the terahertz spectral regime. The copolarized transmission coefficients were found to exhibit stopbands that shift when either a magnetostatic field is applied or the temperature is increased or both. Depending on spectral location of the stopband, either the magnetostatic field gives coarse control and temperature gives fine control or vice versa. The level of magnetostatic control depends on the magnetostatic-field configuration.