I also don't think he's as uncaring as he seems, its just he's not one to show it one, or maybe he doesn't know how to show it, because in the book he mentions how his house "was just the right size when maman was here." it shows that he actually kind of misses her, it makes him notice that his house is kind of empty.
He kind of reminds me of a movie i saw once Garden State. The main character Andrew Largeman (Zach Braff) is a kind of emotionless guy, he himself didn't show any sadness at his own mother's funeral, and in a dream he had he was apathetically sitting in a crashing air plane, but in the end he did start showing his feelings more, and that's what i think is going to happen to Meursault, when things get to a high point or maybe after that high point, he's going to express himself more.