A new method is developed for suppressing thermally induced wavefront distortions of the radiation in the active element of disk geometry. The method is based on controlling radial temperature gradients in the active element using a profiled heatsink. An active element with a zero thermal lens developed on the basis of numerical simulation was experimentally demonstrated in a disk laser head. Higher-order phase aberrations in the active element with a profiled heatsink were weaker than in the element with a flat heatsink. Using this method, a thermal-lens-free active-mirror Yb:YAG amplifier with an output energy of 54 mJ at an average pump power of 100 W and a repetition rate of 106 Hz was implemented.