Official government accounts say the blaze began when melted aluminium from a faulty air conditioner ignited paper on the floor of the warehouse.
The fire then spread into the rafters of the industrial building and across to the day care centre.
Soon after the incident, Felipe Calderon, the Mexican president, ordered an investigation into the fire.
But building safety standards continue to be questioned after previous deadly incidents.
In 2000, a fire killed 21 people at a Mexico City nightclub that only had one available exit, lacked smoke detectors and did not have enough fire extinguishers.
The emergency exit had been locked with a chain.
Last year, 12 people died in a police raid at another Mexico City nightclub. Officers blocked the crowded club's lone working exit, creating a deadly stampede.