We propose an iterative receiver for a multi-carrier (MC) code division multiple access (CDMA) system in the uplink for users moving at vehicular speed. MC-CDMA is based on orthogonal frequency division multiplexing (OFDM), thus time-variant channel estimation can be performed for every subcarrier independently. The variation of a subcarrier over the duration of a data block is upper bounded by a maximum Doppler bandwidth which is determined by the maximum velocity of the users and the carrier frequency. We exploit results from the theory of time-concentrated and bandlimited sequences and apply a Slepian basis expansion for time-variant subcarrier estimation. The Slepian basis functions are determined by two parameters, the block length and the maximum Doppler bandwidth. This approach enables time-variant channel estimation without complete knowledge of the second-order statistics of the fading process. The performance of the iterative receiver is validated for a wide range of velocities by simulations.