How is it thermodynamically possible to obtain energy from a piece of coal?
Coal in open air can and does sponstaneously combust.  

See for example Spontaneous Heating and Fire in Coal Mines and Coal’s Spontaneous Combustion Problem.

At low temperature the change in Gibbs free energy of coal oxidation is still strongly negative, just like at high temperature.

But at low temperature, the reaction rate is low.  

Still, if the rate at which heat is dissipated is less that the rate at which heat is produced, temperature increases and the reaction rate increases until there is appreciable combusiton.