Linear transmission of state measurements is studied, where the control center (CC) sends random state measurement requests to multiple sensors. Each sensor is capable of measuring multiple system parameters, and the CC asks for a particular system parameter from each sensor at each time slot. Delay constrained linear transmission of these measurements over orthogonal fading channels is considered. The total meansquare error (MSE) distortion is studied for Gaussian states and channels under an average power constraint. For a particular symmetric scenario, a round-robin scheduling algorithm and optimal linear transmission (LT) scheme are presented. It is shown that, as opposed to the case of a single parameter measurement, the performance of the proposed LT strategy improves as the delay constraint is relaxed, and achieves the Shannon lower bound under certain matching conditions between the source and the channel statistics.