The local structure of molybdenum dichalcogenide MoX2 (X = S, Se, Te) single crystal has been studied by means of multi-edge (Mo, Se, and Te K-edges) extended x-ray absorption fine-structure spectroscopy as function of temperature. The temperature dependences of the interatomic distances Mo-X, Mo-Mo and X-X (X = S, Se, and Te) and of the corresponding Debye-Waller factors have been extracted over the 70-500 K temperature range. Exploiting the correlated Einstein model, we found that the Einstein frequencies of Mo-X and X-X bonds obtained by present data are in close agreement with the frequencies of the optical (Raman and infrared) stretching modes for both MoS2 and MoSe2, whereas a significant deviation has been found for MoTe2. A similar anomaly has been found for the force constants related to the Mo-X bonds in the MoTe2 case. Our findings, accordingly with the results reported in a recent theoretical paper, support the idea that the optical vibrational modes have a dominant role in MoS2 and MoSe2, whereas the effects of acoustic vibrational modes cannot be neglected in the case of MoTe2.