Describe the relationship between the materials and amount of thermal energy transfer?

If you mean how much heat it can transfer as a thermal mass - in order to move heat from one place to another:

Typically the relationships are given by specific heat capacity (at different temperatures) and latent heats, plus the end-point temperatures to determine which of these conversion factors are relevant.

If time comes into it, you are looking at including shape and thermal conductivity at the minimum, so you really would need to be more specific

Explanation:

the answer is to check all of them! they all apply well at least i think so!

there is no correct list among the choices you've provided.

the list might look something like this:

-- baby human

-- piccolo

-- flute

-- soprano singer

-- trumpet

-- tenor singer

-- trombone

-- baritone singer

-- baritone horn

-- bass singer

-- tuba

since i had to make up the list myself, i made it easy on myself, and i didn't try to shuffle the string instruments and woodwinds into it too.