The Earth's climate sensitivity to radiative forcing remains a key source of uncertainty in future warming projections. There is a growing realization in recent literature that research must go beyond an equilibrium and CO₂‐only viewpoint, toward considering how climate sensitivity will evolve over time in response to anthropogenic and natural radiative forcing from multiple sources. Here the transient behavior of climate sensitivity is explored using a modified energy balance model, in which multiple climate feedbacks evolve independently over time to multiple sources of radiative forcing, combined with constraints from observations and from the Climate Model Intercomparison Project phase 5 (CMIP5). First, a large initial ensemble of 10⁷ simulations is generated, with a distribution of climate feedback strengths from subannual to 10²‐year timescales constrained by the CMIP5 ensemble, including the Planck feedback, the combined water vapor lapse rate feedback, snow and sea ice albedo feedback, fast cloud feedbacks, and the cloud response to sea surface temperature adjustment feedback. These 10⁷ simulations are then tested against observational metrics representing decadal trends in warming, heat and carbon uptake, leaving only 4.6 × 10³ history‐matched simulations consistent with both the CMIP5 ensemble and historical observations. The results reveal an annual timescale climate sensitivity of 2.1 °C (ranging from 1.6 to 2.8 °C at 95% uncertainty), rising to 2.9 °C (from 1.9 to 4.6 °C) on century timescales. These findings provide a link between lower estimates of climate sensitivity, based on the current transient state of the climate system, and higher estimates based on long‐term behavior of complex models and palaeoclimate evidence.