Picosecond geminate recombination kinetics for electrons generated by multiphoton ionization of liquid water become power dependent when the irradiance of the excitation light is greater than 0.3-0.5 TW/crn(2) (the terawatt regime). To elucidate the mechanism of this power dependence, tri- 400 nm photon ionization of water has been studied using pump-probe laser spectroscopy on the pico- and femtosecond time scale;. We suggest that the observed kinetic transformations are caused by a rapid temperature jump in the sample. Such a jump is inherent to multiphoton ionization in the terawatt regime, when the absorption of the pump light along the optical path becomes very nonuniform. The heating of water is substantial (tens of degreesC) because the 3-photon quantum yield of the ionization is relatively low, ca. 0.42, and a large fraction of the excitation energy is released into the solvent bulk as heat. Evidence of the temperature jump is the observation of a red shift in the absorption spectrum of (thermalized) electron and by characteristic "flattening" of the thermalization dynamics in the near-IR The temperature jump in the terawatt regime might be ubiquitous in multiphoton ionization of molecular liquids. The implications of these observations for femtosecond pulse radiolysis of water are discussed.