High Temperature Limit: Equal Probability of Energy States Explained

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Suppose you have a system with different energy states and assume that it is in contact with a heat resevoir (i.e. you know the average of the total of the system). In this case, no matter the system, it seems a general property that in the high temperature limit all energy states become equally probable. Today I saw the example of an electron in a magnetic field.
I must admit I don't have a lot of intuition for what temperature actually is. I can only see from the math that it is a Lagrange multiplier which has the property that 1/T = ∂S/∂U where U is the average total energy.
Now in the high temperature limit this says the change in entropy per change in average total energy is small. But how does this explain the equal probability of different energy states, and how is the equal probability in all explain using the ideas of maximum entropy?

 

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With a high energy, the entropy is large, but the entropy change with changing energy gets smaller. You have many states available anyway, some additional states don't change the entropy so much any more.