The normal electronic-state out of which unconventional superconductivity in UTe2 emerges, is studied using anisotropic high-resolution thermal expansion, magnetostriction, heat-capacity, magnetization and resistivity measurements. Clear thermodynamic signatures of a broad anomaly around 12 K is found in all measurements, and the scaling of the resistivity with the specific heat suggests short-ranged magnetic fluctuations as the origin. We were able follow this ‘12 K anomaly’ to high-fields using previously published resistivity data [Knafo et al. arXiv:2007.06009], and the resulting H-T phase diagram for all three field directions is very reminiscent of other ferromagnetic U-based superconductors. Additionally, thermal expansion and magnetostriction predict the largest pressure effect for c-axis uniaxial pressure and a suppression of the 12 K anomaly with pressure. The electronic Grüneisen parameter is found to take on a moderately large value of around -30.