Temperature, response functions to temperature at mm-wavelengths and magnetic field strength in a 2D-cut of a Bifrost simulation. Panel a: temperature (clipped at 15 000 K) as a function of optical depth; the solid and dashed lines are the maximum response in each column at 1.2 mm and 3 mm respectively (smoothed for visibility), and the filled contours enclose the R_λ at half-peak; the peak response the core of Mg II h is shown for comparison (dash-dotted). Panel b: magnetic field strength for context; panels I–IV: normalized response functions of the 1.2 mm- (solid) and 3 mm- (dashed) continuum and temperature profile (dotted line) at the selected columns in panels a,b).