Yes, it is なか. Slightly more generally, adjective + 中 meaning in the middle of adj. is read なか as far as I can think of. E.g. 忙しい[中]{なか}, 天気の悪い[中]{なか}.
More generally, there is probably no clear rules, i.e., it depends on words whether it is ちゅう or じゅう or なか (じゅう and ぢゅう are not distinguished in modern Japanese).
A basic difference is that なか/ちゅう means in the middle of while じゅう means throughout, all over (some range), but not entirely correct. For example, 午前[中]{ちゅう} can mean both (午前中誰か来た/午前中はいません). A further complication is 午前[中]{ちゅう}[中]{じゅう} is possible at least colloquially (maybe a bit odd, but definitely understood). Also, 午後[中]{じゅう} is the only possibility which means throughout the afternoon. Some time in the afternoon is simply 午後 and never 午後[中]{ちゅう}.
Some more examples: [海中]{かいちゅう} = inside the sea; [海中]{うみじゅう} = all over the sea (as far as can be seen); [山中]{やまなか} = [山中]{さんちゅう} = (somewhere) inside the mountain; [山中]{やまじゅう} = all over the mountain.
Relevant threads on or off this SE.