When two objects are touching, thermal energy transfers from...
hotter to colder substances?
Or
colder to hotter substances?

According to the laws of thermodynamics, Molecular movements of particles will tend to move into state of lower energy and this would mean that knowing the vibrational and translational energy of complex molecules will lose and give off energy usually in the form of heat but also sound and other transferable mediums it will tend to become less energetic and this mobile indicative of colder objects, if examining the average Molecular kinetic energy and bond energies of the compounds in question.