The mistake is that air in Transient Thermal is fixed in space and heat can only conduct through the air. As you may know, air is a very good insulator if it can't move, but a very poor insulator if it can move. To model the movement of air in an oven, use Fluent.
If you don't want to use Fluent, you can have a model in Transient Thermal of just the jig but no air. Put Convection boundary conditions on all faces of the jig and use the Tabular Data to type in the air temperature vs time profile for the heating cycle. Note that the Film Coefficient should be slightly different on faces of the jig that are vertical vs horizontal for the case where the oven does not have a fan to move the air around.