The thermal shifts undergone by the first moment of the ⁶A_1g(S) to ⁴T_1g(G) excitation band and the associated emission band of Mn²⁺-doped ABF₃ perovskites are investigated in the 9-300 K temperature range. It is found that these shifts are similar for the whole series and have average values of +150 and +450 cm^-1 for excitation and emission, respectively. Both the sign and the magnitude of these different thermal shifts are explained in terms of (i) the phonon assistance mechanism required to gain intensity of the parity-forbidden transitions, (ii) the quadratic electron-phonon coupling and (iii) thermal expansion effects. To achieve this analysis a previous discussion upon the nature of the vibrational modes seen in the optical spectra is carried out. It is stressed that the impurity vibrational mode displaying h(cross) omega _g=570 cm^-1 in the emission spectrum of KMgF₃:Mn²⁺ exhibits a value of 540 cm^-1 in the corresponding excitation spectrum. This situation, which is also found for other modes seen in the optical spectra of KMgF₃:Mn²⁺, indicates that the mode (though associated with the LO₃ branch of KMgF₃) is not a pure mode of the lattice but displays a kind of resonant character. As a salient feature the calculated thermal shifts are based on the experimental shifts experienced by the frequencies of the optical and acoustic modes on going from the ground ⁶A_1g to the excited ⁴T_1g state of MnF₆^4-. At variance with findings for the R lines in Cr³⁺ and V²⁺, it is clearly demonstrated that the explicit and implicit contributions to the thermal shift of the zero-phonon line in MnF₆^4- are similar and both induce red shifts upon heating. Moreover the present analysis reveals that the explicit contribution to the thermal shift undergone by the zero-phonon line of KMgF₃:Mn²⁺ is mainly dominated by the odd-parity low-energy modes. The calculated thermal shifts reproduce reasonably well the experimental data.