High-intensity focused ultrasound (HIFU) is a rapidly developing medical technology that allows non-invasive thermal ablation of tumors. Thermal treatment of liver tumor, which is one of the most common malignancies worldwide, is problematic because large blood vessels act as a heat sink. Convective cooling protects the cancer cells from thermal destruction and decreases the necrosed volume. A major objective of the method development is to achieve a virtually complete necrosis of tumors close to major blood vessels and to avoid blood vessel damage and, hence, the needed treatment planning. The present study is aimed at predicting liver tumor temperature during HIFU thermal ablation in a patient-specific liver geometry. The model comprises the nonlinear Westervelt equation and bioheat equations in the liver and blood vessels. The nonlinear hemodynamic equations are also taken into account with the convected cooling and acoustic streaming effects being taken into account. We found from this three-dimensional three-field coupling study that in large blood vessels, both convective cooling and acoustic streaming may change the temperature considerably near the blood vessel. More precisely, acoustic streaming velocity magnitude can be several times larger than the blood vessel velocity. The results presented in the current work can be further used to construct a surgical planning platform.