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There are two points relevant for the discussion: air itself carries a very small amount of thermal energy and it is a very poor thermal conductor. For the first point, I think it is interesting to consider the product $\text{density} \times \text{specific heat}$, that is the amount of energy per unit volume that can be transferred for every $\text{K}$ of temperature difference.
$\begingroup$ So I had a huge debate about this with my friends. Imagine that you are in a non-inertial frame of reference. For simplicity, assume that frame is accelerated along x-axis. You have held a charge in your hand and hence it is rigidly bound to your body. I am in an inertial frame and I see you accelerated and so I see the radiation coming out from the charge. Would you also see the radiation coming out from the charge even though it is at rest with respect to you?
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