I used a rectangular worm bin like you describe for years in east Oakland, Ca. When it would get hot and dry in the long summers, I would notice the worm population decreasing, they would migrate to the bottom and out of the bin into the surrounding soil. As the temp increases and the moisture dropped, I would start to see these large grubs (maggots) thriving in the upper layers. At first I was worried, but then I found the source, black soldier fly! They had found my bin and set up their nursery. These grubs are compost shredders! they seem to eat up scraps faster than the worms do, are an excellent protein source for the chickens, and make great compost.
After observation and research, rather than try to micromanage the climate for worms, I thought it better to allow different organisms to do the work according to the seasons. In the summer I would have more black soldier fly, and in the wet season, more worms. The flys, when they mature, are long bodied, slow moving flies. They do not fly in your face or bother the animals, and cause no nuisance. I don't know if they would naturalize in your climate, but I recommend observing and identifying the organisms in your compost, and allowing access to more insects than just worms. I designed my bin to keep out rodents and other mammals and birds, but allowing the worms and other bugs to come and go as they please. Diversity is just as important in compost as it is in the garden or landscape.
