They will typically choose the hide they are more comfortable in over a hide that is the right temperature. In your case, I'd replace the half log with a second Exo Terra hide - put one on the warm side and one on the cool side. With his security choices being identical, he'll likely go wherever the temperature is best for him at that time.
I agree, or get a second (identical) half log if that's what he prefers. It's important to offer the same hides in both the warm and cool zone, just so they don't choose a favorite hide over thermoregulation.