The diffuse soft X-ray emissivity from galactic winds is computed during the Epoch of Reionization (EoR). We consider two analytic models, a pressure-driven wind and a superbubble model, and a 3D cosmological simulation including gas dynamics from the First Billion Years (FiBY) project. The analytic models are normalized to match the diffuse X-ray emissivity of star-forming galaxies in the nearby Universe. The cosmological simulation uses physically motivated star formation and wind prescriptions, and includes radiative transfer corrections. The models and the simulation all are found to produce sufficient heating of the intergalactic medium to be detectable by current and planned radio facilities through 21 cm measurements during the EoR. While the analytic models predict a 21 cm emission signal relative to the cosmic microwave backgroundsets in by ztrans ≃ 8-10, the predicted signal in the FiBY simulation remains in absorption until reionization completes. The 21 cm absorption differential brightness temperature reaches a minimum of ΔT ≃ -130 to -200 mK, depending on model. Allowing for additional heat from high-mass X-ray binaries pushes the transition to emission to ztrans ≃ 10-12, with shallower absorption signatures having a minimum of ΔT ≃ -110 to -140 mK. The 21 cm signal may be a means of distinguishing between the wind models, with the superbubble model favouring earlier reheating. While an early transition to emission may indicate X-ray binaries dominate the reheating, a transition to emission as early as ztrans > 12 would suggest the presence of additional heat sources.