I managed to find the answer to my own question. If anyone was curious, the following video was very helpful: https://www.youtube.com/watch?v=x4TXEaAYfMw
My code is as follows:
h1=hgload('T_900K.fig');
h2=hgload('T_1000K.fig');
h3=hgload('T_1100K.fig');
h4=hgload('T_1200K.fig');
h5=hgload('T_1300K.fig');
h6=hgload('T_1400K.fig');
figure
h(1)=subplot(1,1,1);
copyobj(allchild(get(h1,'CurrentAxes')),h(1));
copyobj(allchild(get(h2,'CurrentAxes')),h(1));
copyobj(allchild(get(h3,'CurrentAxes')),h(1));
copyobj(allchild(get(h4,'CurrentAxes')),h(1));
copyobj(allchild(get(h5,'CurrentAxes')),h(1));
copyobj(allchild(get(h6,'CurrentAxes')),h(1));