Kernel density estimate of the probability density function for the line ratios as a function of temperature and average number density along the LOS, for the internally heated clump case with a density distribution ∝ r^−1.5, and a doubled microturbulence level, for lines at around 96.7 GHz (top row, for line ratios I(2₀ − 1₀)/I(2₋₁ − 1₋₁), I(2₁ − 1₁)/I(2₀ − 1₀), and I(2₁ − 1₁)/I(2₋₁ − 1₋₁)), those at around 241.7 GHz (bottom left, ratio I(5₋₁ − 4₋₁)/I(5₀ − 4₀)), and around 338.1 GHz (bottom right, ratio I(7₋₁ − 6₋₁)/I(7₀ − 6₀)). The results for the fiducial values of microturbulence are shown in yellow, for reference.