Bull feathers. The leads would *obviously* (duh!!) screw-up the operation of
the antenna (unless you're proposing fibre optic temp sensors).

Actually, the real problem is that the RF can screw up the very sensitive
probe.

The trick is to do on-offs of antenna power, and register the temperature on
the offs. The duty cycle must be adjusted so that the equilibrium temperature
is being sampled properly. Most of the time, the temp drops noticeably after 30
seconds to a minute. In some cases, the probe can be quickly attached and then
detached during the off cycle.

It's fun to do. Som experimenting shows how to mitigate 'to measure is to
disturb' issues.

Best,
Chip N1IR