Perception of vocalizations and other behaviorally relevant sounds requires integrating acoustic information over hundreds of milliseconds. Sound-evoked activity in auditory cortex typically has much shorter latency, but the acoustic context, i.e., sound history, can modulate sound evoked activity over longer periods. Contextual effects are attributed to modulatory phenomena, such as stimulus-specific adaption and contrast gain control. However, an encoding model that links context to natural sound processing has yet to be established. We tested whether a model in which spectrally tuned inputs undergo adaptation mimicking short-term synaptic plasticity (STP) can account for contextual effects during natural sound processing. Single-unit activity was recorded from primary auditory cortex of awake ferrets during presentation of noise with natural temporal dynamics and fully natural sounds. Encoding properties were characterized by a standard linear-nonlinear spectro-temporal receptive field (LN) model and variants that incorporated STP-like adaptation. In the adapting models, STP was applied either globally across all input spectral channels or locally to subsets of channels. For most neurons, models incorporating local STP predicted neural activity as well or better than LN and global STP models. The strength of nonlinear adaptation varied across neurons. Within neurons, adaptation was generally stronger for spectral channels with excitatory than inhibitory gain. Neurons showing improved STP model performance also tended to undergo stimulus-specific adaptation, suggesting a common mechanism for these phenomena. When STP models were compared between passive and active behavior conditions, response gain often changed, but average STP parameters were stable. Thus, spectrally and temporally heterogeneous adaptation, subserved by a mechanism with STP-like dynamics, may support representation of the complex spectro-temporal patterns that comprise natural sounds across wide-ranging sensory contexts.