Dear friend,
it looks like you are getting close to experiments!
Detecting hot spots in a dielectric block from a close distance like you indicated would be best with a horn antenna.
Its gain is not important but its main lobe width is; also inside of the block, the beam width may become narrower by one/sqr root of lambda. The incidence angle to block wall may squint the beam, etc.
The answer to your problem I think is best answered by experiment. Take a standard-gain horn, install a test hot spot in the block (easiest may be using deionized distilled water) and run several test scans. From the results you can calibrate the setup, find how the block permittivity distorts the beam, and test your temperature resolution.
The short distance between your horn aperture and block wall will cause mismatch which may be difficult to handle, mainly if it changes. Often the horn aperture is directly touching the wall (making it an applicator), then the mismatch can be made fixed and easier taken into account. In applicators, some experimenters filled the horn cavity with a dielectric (Alumina powder, etc.) to make the air/dielectric transition less mismatched.