Thomson scattering (TS) diagnostics provide reliable, minimally perturbative measurements of fundamental plasma parameters, such as electron density (ne) and electron temperature (Te). Deep neural networks can provide accurate estimates of ne and Te when conventional fitting algorithms may fail, such as when TS spectra are dominated by noise, or when fast analysis is required for real-time operation. Although deep neural networks typically require large training sets, transfer learning can improve model performance on a target task with limited data by leveraging pre-trained models from related source tasks, where select hidden layers are further trained using target data. We present five architecturally diverse deep neural networks, pre-trained on synthetic TS data and adapted for experimentally measured TS data, to evaluate the efficacy of transfer learning in estimating ne and Te in both the collective and non-collective scattering regimes. We evaluate errors in ne and Te estimates as a function of training set size for models trained with and without transfer learning, and we observe decreases in model error from transfer learning when the training set contains ≲200 experimentally measured spectra.