Temperature: Like herps, roaches can thermoregulate. If you provide vertically stacked egg flats, it creates the most surface area, allows frass/shed skins/dead bodies to accumulate on the bottom, and allows heat to rise from the bottom of the bin upwards. I use heat tape to heat my bins from the bottom, and the roaches can then choose to climb higher to cool down or stay at the bottom for warmth. I think their greatest reproduction is achieved in the 85-95 degree F range.

As Carlos said (and linked to) roaches do not need a high protein diet, this is a common myth that is perpetuated on the interwebs. Excess protein in the diet results in uric acid production, which can have detrimental effects on both the roach colony and on the animals that subsequently feed on them. Feed your roaches a good grain based gutload and offer a variety of fruits, veggies and greens to act as both a nutrient and moisture source. As long as they are warm, have space, have plenty of food, and are unstressed (leave them alone, preferably in darkness as much as possible) your colony will grow.