We report an in situ thermal study of Yb-doped fluorite crystals Yb:CaF(2) and Yb:SrF(2) under high power pumping, with or without laser operation. The experiment combines simultaneously thermography and measurement of the thermal aberrations. This setup allows us to measure temperature gradients, thermal lens, and absorption coefficients. From these measurements, we evaluate the thermal conductivity, fractional thermal load, and thermo-optic coefficient. Great differences are observed between the lasing and non lasing regimes. Our measured thermal lenses are greater than what are expected from the thermo-optic parameters found in previous work. Based on this thermal study, we design a laser cavity operating with large output power and TEM(00), leading to better performances for Yb:CaF(2) than Yb:SrF(2).