Example solution (for arbitrary mass loss rate) of the radiative transfer equation assuming a non-constant temperature, shown in red. The black line represents the result for the constant temperature solution. The initial temperature is set to T = 10⁶ K in both cases. The density is n = 2 × 10¹⁰ cm^-3. The difference in both spectra is not strongly pronounced. The “peak” at lower frequencies in the red curve results from numerical issues. The arrows mark the upper limits of the observational radio fluxes of π¹ UMa in both frequency bands.