What if I have a temporary appointment in between two fixed-term appointments, would the period on temporary appointment be treated as continuous?

The period of service on a temporary appointment would constitute a break in the continuity of service under a fixed-term appointment, therefore your overall period of service would not be considered continuous. The period of service under a temporary appointment would not count towards the five-years of qualifying service. And the count of qualifying years of service would start counting from the date of your second fixed-term appointment, posterior to the period on temporary appointment.