Weak anharmonic coupling of two soft molecular vibrations is shown to cause pronounced temperature dependence of the corresponding resonance Raman bands. The developed theory is used to interpret the temperature dependence of the iron-histidine band of deoxyheme proteins and model compounds. It is shown that anharmonic coupling of the iron-histidine and heme doming vibrations must cause pronounced broadening of the band, its asymmetry, and shift of its maximum to the red upon heating. It also can lead to a structured shape of this band at room temperature. Proper consideration of the anharmonic coupling allows simulation of the temperature dependence of the iron-histidine band shape of horse heart myoglobin in the temperature interval of 10-300 K, using the minimum number of necessary parameters. Analysis of this temperature dependence clearly shows that the iron-histidine band of deoxyheme proteins is sensitive to the glass-liquid phase transition in the protein hydration shell, which takes place at 160-190 K.