In Chapter One, Mersault cleans up a bit before the funeral procession. Mersault refuses to look at his mother before the casket is sealed, signs forms, and the procession in underway. It consists of himself, the nurse, the director, the undertaker's men, the priest, and Monsieur Pérez, a member of the home who is allowed to attend because of his closeness to Maman. The procession walks along the long road to the village, nearly an hour away. Mersault feels he can understand his mother better when he is told that she and Pérez would take walks often to the village. Pérez begins to fall behind but catches up using shortcuts. Mersault complains of the heat. He notes that the entire funeral moved so fast and deliberately that he remembers nothing except a comment of the nurse and the image of Pérez crying.
The heat made the procession difficult, as well as the heat's effects on things around him.
"And then there were the smells, smells of hot leather and horse dung from the hearse, veined with whiffs of incense smoke. What with these and the hangover from a poor night’s sleep, I found my eyes and thoughts growing blurred."
After the funeral, he was exhausted. I can understand this in terms of emotional stress. Unfortunately, Mersault really doesn't have any emotional feelings. I believe he's just happy it's over and disengaged.