Towel construction and moisture affect how warmth feels after removal from the rack.
A towel that cools quickly after removal does not by itself establish a towel-warmer fault. Once removed, it no longer receives heat from the rack. Compare with a normal dry bath towel, following the warmer’s instructions for placement, towel quantity and warm-up time.
A purpose-made cooling towel is a different product: for example, MISSION describes its cooling fabric as enhancing evaporation when activated with water. That does not mean every microfiber or PVA towel behaves identically, or that a wet cotton towel is guaranteed to stay warm.
If the rack itself is not heating, use the troubleshooting instructions for its exact model. Do not cover it with excessive layers or exceed its permitted towel load to compensate for a towel that cools quickly.
Sources: MISSION cooling-towel explanation and Infinity towel-warmer use and safety instructions (use the manual supplied with your own warmer).