Temperature profiles of short (L_f < 9 Mpc), medium-length (9 ≤ L_f < 20 Mpc), and long filaments (L_f ≥ 20 Mpc) in orange, green, and blue, respectively. The thick solid lines with circles correspond to the temperature profiles presented in Sect. 4.2, while the thin dotted lines with squares show the results in which contributions of galactic haloes are included (see Sect. 5). For each case, the horizontal grey lines represent the average temperatures of all the gas cells (CPmax points excluded) in the box. These profiles clearly show the isothermal cores of filaments.