i can't think of an energy-related reason to insulate an interior wall unless:

1. there's a big temperature or humidity difference between two adjacent spaces (e.g., at a sauna or hot tub room)

2. you're using a wall in a trombe-wall-like way to gather and store heat and want to buffer it from an adjacent cool/conditioned space.

If you want it for sound insulation....so you don't hear your granda and her 24 year old boyfriend going at it in the adjacent bedroom....
I guess you could say it keeps the heat down....

I could see it in a situation where you have seasonal/infrequent use parts of a building which are maintained at a 'not freezing but not comfortable' temperature when not in use. Insulating this zone from the rest of the building would maximize your efficiency, but at that low of a temperature differential it may not be worth it.

no

Insulation of interior walls is primarly for sound isolation...but you have to do all the other things with the insulation to really make it work. Noise like water takes the path of least resistance.

I could see it having benefit if you had a sunroom or greenhouse type area that you wanted to let get warmer than the rest of the house. And normally when you've got a garage, you don't insulate the garage, but instead insulate the walls between the garage and the rest of the house.

But other than that, not really.

it actually does help for heat transmission as well as sound

but for what reason, mdler?

Ooops. I read insulting interior walls.

The only insulation which really counts for energy savings as far as I know from running a number for "mec check". is insulating between a basement floor and first floor. For some unknown reason this gives you higher values and allows you to have more square footage of glass. It is something we have to submitted with building plans, but no one is really sure how damn accurate it is and who is actually the one to do the calculations. Sometimes the mechanical contractor will under take the task, sometimes the window supplier with undertake the task, sometimes no one will undertake the task. Which is usually when it is a big ass house loaded with glass. It is of course this type of house which the press and the AIA is all over for giving awards.