How does thermal energy from the flame get to the molecules in the ice cubes?

Nothing in your question suggests any particular answer.

Energy is not a physical unit. It is a philosophical concept and an accounting technique used to analyze mechanical and chemical exchanges. In nuclear physics it is defined as a wavelength of light, in biology it is a synonym for metabolism, and in public utilities they say energy when they mean connectivity. Anybody who uses the word in any other context either does not know what he is talking about, or is peddling something you don't need.

"Thermal energy" is simply heat.