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Test-mass thermal noise is a limiting noise source for current and next-generation ground-based gravitational-wave observatories in their most sensitive frequency band. In addition to ongoing efforts to reduce coating mechanical loss, complementary approaches such as the use of uniform-intensity laser beams, including higher-order Laguerre─Gaussian (LG) and Hermite─Gaussian (HG) modes, have been proposed as alternatives to the fundamental Gaussian beam due to their thermal-noise advantages. As the interferometer operating power increases toward the megawatt regime, as anticipated for next-generation detectors, thermal aberrations arising from absorption in the high-reflectivity coatings of the test masses become an increasingly severe challenge. In parallel, the spatially more extended intensity profiles of higher-order modes, which enable their thermal-noise benefits, modify the thermal loading of the test masses, making it essential to assess their behavior under absorption-induced self-heating. In this work, we quantify the robustness of higher-order incident beams against thermal deformation. We show that, under identical operating conditions, higher-order modes produce significantly more uniform thermally induced mirror distortions compared to the sharply peaked aberrations generated by the fundamental mode. As a result, substantially less thermal compensation power is required for their active correction, with the required optimal curvature correction reduced to 33% of that of the fundamental mode for the <inline-formula><mml:math><mml:msub><mml:mi>LG</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> mode and to 24% for the <inline-formula><mml:math><mml:msub><mml:mi>HG</mml:mi><mml:mrow><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn></mml:mrow></mml:msub></mml:math></inline-formula> mode. In addition, we show that the residual thermal deformation for higher-order modes leads to significantly lower optical power loss and enables larger power buildup and enhanced modal purity in an aLIGO-like optical cavity. We further demonstrate that astigmatism compensation enhances the intracavity modal purity of HG modes under self-heating-induced thermal deformation. These results highlight that higher-order laser modes mitigate thermal noise while intrinsically suppressing beam self-heating-induced thermal distortions, making them more thermally robust and well suited for operation in high-power gravitational-wave interferometers.