The person who is using his parietal lobe is Al.
The parietal lobe has two main function according to its region. The first function is to receive and process sensory information from all parts of the body while the second is to interpret visual information as well as processing language and numerical inputs.
As described in the question, Al is trying to determine whether the shower is hot enough, which means that he is using his parietal lobe to do so.
