I never use the heating core and I have baked that size pan many times.Just make sure you bake it long enough until the middle is done and it should be fine!!
I din't have a propper heating core so I always use flower Nails .
They work really well , just grease them and place flat side down before you add your batter . I use 2 for the 11x15 so you will probably need more than that
I use one flower nail right in the center of my pan that size.... I use a pan coating that I make (1 cup of Crisco, 1 cup of flour and one cup of vegetable oil) and coat the flower nail really well. Place it upside down in the center of your pan and pour your cake mix in... works really well 
I've done several 12x18 and never used a heating core and they came out great each time.
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