We report the first demonstration of a Yb:YAG thin disk laser wherein the gain medium is intracavity face-cooled through bonding to an optical quality SiC prism. Due to the particular design of the composite bonded Yb:YAG/SiC-prism gain element, the laser beam impinges on all refractive index interfaces inside the laser cavity at Brewster's angles. The laser beam undergoes total internal reflection (TIR) at the bottom of the Yb(10%):YAG thin disk layer in a V-bounce cavity configuration. Through the use of TIR and Brewster's angles, no optical coatings, either anti-reflective (AR) or highly reflective (HR), are required inside the laser cavity. In this first demonstration, the 936.5-nm diode pumped laser performed with approximately 38% slope efficiency at 12 W of quasi-CW (Q-CW) output power at 1030 nm with a beam quality measured at M(2) = 1.5. This demonstration opens up a viable path toward novel thin disk laser designs with efficient double-sided room-temperature heatsinking via materials with the thermal conductivity of copper on both sides of the disk.