Doughnut-shaped laser beams have applications in laser-based additive manufacturing, laser heating of diamond anvil cells, and optical super-resolution microscopy. In applications like additive manufacturing and heating of diamond anvil cells, a doughnut-shaped beam is frequently used to obtain a more uniform temperature profile relative to that generated by a conventional Gaussian beam. Conversely, in super-resolution microscopy, the doughnut-shaped beam serves to enhance spatial resolution and heating is an undesirable side effect that can cause thermal damage. Here, we develop analytical expressions for the temperature rise induced by a doughnut-shaped laser beam both alone and in combination with a Gaussian beam. For representative, experimentally determined beam radii and a wide range of thermal properties, we find that a doughnut-shaped beam results in a peak temperature rise no more than 90% and often less than 75% of that for a Gaussian beam with the same total power. Meanwhile, the region of the sample surface that reaches 80% of the maximum temperature rise is at least 1.5 times larger for a doughnut-shaped beam than for a Gaussian beam. When doughnut-shaped and Gaussian beams are applied simultaneously, the ratio of the maximum temperature rise for the two beams combined vs a Gaussian beam alone can be up to 2.5 times lower than the ratio of the doughnut-shaped vs the Gaussian beam power. For applications like super-resolution microscopy that require high doughnut-shaped laser beam powers, the doughnut-shaped beam intensity profile is thus advantageous for minimizing the total peak temperature rise when applied together with a Gaussian beam.