It’s true that visible light has more energy per photon than infrared, but two key variables here are being ignored.
Firstly, almost everyone has experienced the heat of a light bulb from the light shining on them. In that scenario, it’s the infrared instead of the visible light heating you up. However, it’s because most light bulbs are so inefficient that most of the light emitted is in the infrared instead of visible light spectrum. One photon of visible light has more energy than infrared, but there’s much more infrared coming out.
Is it due to the energy level transitions and their characteristic energies?
Secondly, you’re sort of on track here. The absorption of the wavelengths of light varies across the spectrum. To put it in context, this means in simple terms that the energy transitions made in the absorption of a higher energy photon like visible light are different from the lower energy ones of infrared. The lower energy transitions are associated more with the vibrations (and thus heat energy) of the molecule, while the higher energy ones are more electronic in nature.