First of all, there is nothing that stops a department from converting a temporary position to permanent status. It is just a matter of paperwork and signatures.
That being said, for a position to be converted from temporary to permanent through the CUPEU collective agreement, it must have existed for 36 months or longer. An employee who has occupied such a position for 36 or more months is automatically converted to permanent status -- assuming he holds the necessary qualifications for the position. An employee who has filled such a position for less than 36 months is not automatically converted; instead, the position must be posted and the employee must apply.