Killies can breed in both peat and mops. not uncommon.
King Killies however, I am uncertain, but more than likely there were eggs in the mop you moved over to the other tank.
males should begin to colour up when they are around 10mm long with the prominance being in the fins. of course it will be easier to sex when they are bigger.
With regards to temperatures determining sex.... well yes this does happen, but to what the temperature ranges are, I am uncertain. Alan new, but I think casserole would have an idea about this.
hope that helps