Amount of heat (heat differential) 
Composition of the solid (what it's made out of) 
Density of the solid (closer the atoms are, the higher the rate) 
The medium with which heat is transferred to the solid (hot air would take longer to transfer heat to and through than hot oil)
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When the heat passes through a solid, the effect is that the solid will only become hot or warm ( base on the heat passing thruogh )
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