The thermodynamic properties of the photomagnetic Prussian blue analog K0.3Co[Fe(CN)6]0.77 · 4.4H2O, which exhibits a charge-transfer induced spin transition (CTIST), are reported. According to the thermal history of the sample, different low-temperature states are obtained: a quenched high-spin state (Q), a low-spin state (LT) achieved through the decay of the Q state, and an "intermediate" state (IM) combining low-spin (LS) and high-spin (HS) local states. The IM state is obtained by slow cooling and displays a slight kinetic dependence. The long lifetime of the IM state, which persists up to the vicinity of the CTIST temperature, is unusual, and differs from all metastable states reported so far for photo-magnetic Prussian blue analogs. The properties of the different states and of their photo-excited counterparts are investigated by magnetic and photomagnetic measurements, calorimetry, diffuse reflectance, and X-ray diffraction. A key feature of the IM state revealed by X-ray diffraction is the onset of phase separation between a LT-type fraction and a mixed HS-LS fraction (approx. 50 : 50). X-ray patterns of the IM state obtained during successive cooling and heating stages document irreversible transformations. The formation and properties of the IM state suggest a self-organization process between low-spin and high-spin sites in response to internal structural stresses, and this effect is hindered by irradiation with visible light. The relaxation kinetics of the Q and photo-excited states are analyzed by using a twovariable model which accounts for the onset of correlations due to short-range elastic interactions. A quantitative comparison to the analogous sodium compound, Na0.32Co[Fe(CN)6]0.74 · 3.4H2O, confirms the non-standard behavior of the title potassium compound and supports the structural origin of the self-organization processes.