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Temporal Curvature Cosmology (TCC) introduces a covariant framework in which curvature of proper time, rather than curvature of spacetime alone, acts as a fundamental driver of gravitation and cosmological evolution. Matter–energy distributions alter the local rate of proper time, producing temporal-curvature gradients capable of reproducing gravitational phenomena without invoking dark matter, dark energy, or inflationary fields. From a Lagrangian formulation, we derive the Temporal Curvature Field Equation (TCFE), linking the temporal curvature scalar 𝒯 to the trace of the energy–momentum tensor through □𝒯 = αT.The resulting dynamics recover the Newtonian limit, remain consistent with post-Newtonian and gravitational-wave constraints, and yield a stable cosmological solution in which entropy flow and causal structure emerge naturally from temporal dynamics.As a phenomenological test, we apply the TCFE to the SPARC galaxy NGC 3198 and obtain a joint fit to both rotation-curve and lensing-proxy behavior without invoking dark matter. The framework therefore provides a unified temporal-geometric description of gravitation together with observationally testable predictions involving redshift drift, gravitational lensing, and clock-rate gradients.