For nuclear reactor components, uniaxial isothermal fatigue curves are used to estimate the crack initiation under thermal fatigue. However, such approach would be not sufficient in some cases where cracking was observed. To investigate differences between uniaxial and thermal fatigue damage, tests have been carried out using the thermal fatigue devices SPLASH and FAT3D: a bi-dimensional (2D) loading condition is obtained in SPLASH and crack initiation is defined as the first 150-μm surface cracks, whereas a tri-dimensional (3D) loading condition is obtained in FAT3D and crack initiation refers to the first 2-mm surface crack. All the analysed tests clearly show that for identical levels of strain, the number of cycles required to achieve crack initiation is significantly lower in thermal fatigue than in uniaxial isothermal fatigue. The enhanced damaging effect probably results from a pure mechanical origin: a nearly perfect biaxial state corresponds to an increased hydrostatic stress. In that frame, a Part II accompanying paper will be dedicated to investigate accurately on multiaxial effect, and to improve thus estimation of crack initiation under thermal fatigue.