Extensive calorimetric studies on the Kondo compound TmS are described. A crystal-field splitting of 25 K is found with a highly degenerate ground state. The magnetic ordering is characterized by the invariance of the linear temperature term of the specific heat through TN and by a broadened anomaly at TN. The magnetic phase diagram has a reentrant shape. Comparisons are made with the intermediate-valence compound TmSe. A new coherent phase appears to occur well below TN. © 1985 The American Physical Society.