How can I read the potential energy diagrams when there is thermal energy?

This is an insightful question with a complicated answer because every system will have a distribution of kinetic energies, and sometimes the system will be able to surmount an energy barrier, but most often not.

You can get an idea of how likely it is for a system to have enough energy to carry out a chemical reaction, for example, by comparing the average thermal energy to the height of the barrier. The average kinetic energy in one coordinate (in this case, the reaction coordinate) at temperature T will be roughly kT (or more commonly, RT on a per mole basis, where R=8.314 J/mol-K). So if the temperature is 500 K, the average kinetic energy along any coordinate is roughly 4.2 kJ/mol.

If you compare the size of the barrier to the average thermal energy, the probability of surmounting the barrier of height #E_A# is approximately equal to the Boltzmann factor #P=exp((-E_A)/(RT))#. So the probability of surmounting a 200 kJ/mol barrier at 500K is #1.3times10^(-21)# (really small!). That's why many reactions require #10^20# attempts or more to get a successful reaction event.