Just some information i found: What you drink goes into your stomach. Your stomach is not connected to your baby whatsoever, and your baby is protected inside a bag of fluid which resists temperature change - you'd have to raise your entire body's core temperature to affect the baby's temperature, and even then, it would not "burn" its skin. The fluids absorbed by your stomach into your bloodstream do not remain hot, they become your body's temperature.
No hot stuff can not burn your body. Go get your hot chocolate girl. For it to burn your baby it would have to be boiling as you drink it.