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A theoretical and experimental study of thermal lensing in Yb-doped crystals is presented. In this first part, we focus on theoretical considerations and we describe an original technique suitable for thermal lensing measurements in end-pumped materials. We first derive an expression of the temperature distribution with account of absorption saturation and pump beam divergence inside the crystal, and we address a more general discussion on the particularities of quasi-three-level lasers, as far as thermal effects and fracture issues are concerned. The thermal lens was then measured using a simple technique based on a Shack-Hartmann wavefront analyzer, under lasing and nonlasing conditions. We demonstrate that the technique allows precise wavefront measurements even on small spots. Thermal lensing measurements are finally presented in Yb-doped YAG, GGG, YCOB, GdCOB, KGW, and YSO crystals.