A heat treatment apparatus and associated method are provided for heating a substrate. The apparatus includes a processing chamber containing a process space, first and second substrate supports, and first and second heating sources. The first substrate support is configured to support the substrate in a spaced relationship with the first heating source to define a heat exchange gap and to transfer heat energy through the heat exchange gap to elevate a temperature of the substrate to an offset temperature below a process target temperature. The second substrate support is configured to support the substrate in a spaced relationship with a second heating source to define a heat exchange gap between the second heating source and the substrate and to transfer heat energy through the heat exchange gap to elevate the temperature of the substrate from the offset temperature to the process target temperature in controlled increments.