We present near-infrared [ 1 -2.3 \mu m ] spectroscopy of the massive intermediate age star cluster W3 in the merger remnant and proto-elliptical galaxy NGC 7252 , obtained with the NTT telescope . This cluster has an age when the integrated near-infrared properties of a stellar population are dominated by the cool and luminous Asymptotic Giant Branch ( AGB ) . We compare the data with instantaneous burst model predictions from new evolutionary synthesis models that include : ( i ) the computation of the evolution through the thermally pulsing AGB ( TP-AGB ) for low- and intermediate-massive stars , with the initial mass and metallicity dependent formation of carbon stars ; ( ii ) spectroscopic data from a new stellar library in which differences between static red giants , variable oxygen rich TP-AGB stars and carbon stars are accounted for . The new evolutionary model predicts that the contribution of carbon rich stars to the luminosities in the near-IR passbands is a strong function of metallicity . The comparison of the data to the models clearly shows that carbon stars are present : for the first time , carbon rich star spectral features are thus detected directly outside the Local Group galaxies . Good fits to the available optical/near-IR photometry and the near-IR spectrum of NGC 7252-W3 are found for an age of 300-400 Myr and A _ { V } \simeq 0.6 - 0.8 . The models show that these parameters depend weakly on the model metallicity in the range of Z/Z _ { \odot } = 0.4 - 1 , with higher likelihood for solar metallicity models . At solar metallicity , a mixture of carbon rich and oxygen rich stars is predicted . The strength of the near-IR molecular bands that originated from oxygen rich AGB stars can be used to constrain the absolute T _ { eff } scale of these objects , i.e . a relation between colour and T _ { eff } . We found that , in the framework of our set of evolutionary tracks , the data are more consistent with the temperature scale calibrated on Long Period Variables than on giant stars . At a given colour , variable AGB stars have a lower T _ { eff } than static ( or quasi-static ) M giants .