  A major problem of state-of-the-art Nb$_3$Sn accelerator magnets is their
long training due to thermo-mechanical perturbations. Increasing the specific
heat, $C_p$, of the Rutherford cable would reduce and/or eliminate training by
limiting the coils temperature rise. This paper studies feasibility of
increasing the $C_p$ of Rutherford-type cables by using thin composite
Cu/$Gd_2$O$_3$ and Cu/$Gd_2$O$_2$S tapes produced by Hyper Tech Research, Inc.
The tape can be either wrapped around the cable, placed on the cable wide faces
under the insulation, and/or inserted as a core. Wire samples outfitted with
these high-$C_p$ ribbons, or tapes, were prepared and tested at FNAL for their
Minimum Quench Energy (MQE). At 90%I$_c$ and 15 T, the average gain of MQE of
the Nb$_3$Sn wire soldered to the Cu/$Gd_2$O$_2$S 55 micrometer thick ribbon
was 2.5, and further increased at larger transport currents.
