Explanation

(b) We can relate an absorbed energy $Q$ and the resulting temperature increase $\mathrm{\Delta}T$ with relation $Q = cm\mathrm{\Delta}T.$ In that equation, $m$ is the mass of the material absorbing the energy and $c$ is the specific heat of the material. An absorbed dose of 3 Gy corresponds to an absorbed energy per unit mass of $3\ J/kg.$ Let us assume that $c$ the specific heat of human body, is the same as that of water, $4180\ J/kg\ K.$ Then we find that
$\mathrm{\Delta}T = \frac{Q/m}{c} = \frac{3}{4180} = 7.2 \times 10^{- 4}K = 700\mu K$
Obviously the damage done by ionizing radiation has nothing to do with thermal heating. The harmful effects arise because the radiation damages DNA and thus interferes with the normal functioning of tissues in which it is absorbed