I do wonder whether having 5 or 6 bins wil mean that you don't have sufficent volume in each one to keep the temperature up. Th heat builds up best in a big heap - if it's too shallow it won't get wam and rot down properly.
Stil, try it and see how you go. We started with a big compost heap of slatted wood, in two sections. Although we had loads of stuff in it the first year (shreddings from tree felling and massive garden clearing etc), after that the second section of the heap got a bit flat. So we divided the bin into four sections instead of two, using two for leaves and two for other compost. In late autumn (any day now) we put a bit of old carpet over this year's heap, to leave it for a year. We then unpack and distribute last year's heap, and use this bin to start over again. If the leaves need longer we just leave them for another season.
Ours gets plenty of sun, but the compost itself should generate the heat it needs. Using a dark coloured covering or lid should help. You'll know when it's ready, as it will look like compost, with few identifiable items in it. Mine always has some sticks and woody lumps that I have to remove as I go along (plus the occasional fork or a potato peeler!), but it's great stuff, and the leaf mould is superb if you leave it long enough.