The charge-density-wave phase transition of 1T-TiSe2 is studied by angle-resolved photoemission over a wide temperature range. An important chemical-potential shift which strongly evolves with temperature is evidenced. In the framework of the exciton condensate phase, the detailed temperature dependence of the associated order parameter is extracted. Having a mean-field-like behavior at low temperature, it exhibits a nonzero value above the transition, interpreted as the signature of strong excitonic fluctuations, reminiscent of the pseudogap phase of high-temperature superconductors. Integrated intensity around the Fermi level is found to display a trend similar to the measured resistivity and is discussed within the model.