"The hot box" was her unique way of referring to the jail in which the fellow had been detained.

Re-reading this first post it hit me that "Hot Box" has a prisoner-of-war connotation, mostly WWII, where a prisoner was placed in a box, sometimes fabricated of metal, in the hot sun.
Terrible.
A Hot Box was featured in the movie "Bridge on the River Kwai" and Alec Guiness, playing the senior British officer, was placed in it to break his spirit.