Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Since the novel is written in the first person, the "tone" is a question of how David portrays himself and the events of his life. As David confesses to his role in the death of Giovanni, the question is: will he go hard on himself or easy?
Before Hella leaves, she says, "I'll soon be gone. Then you can shout it to those hills out there, shout it to the peasants, how guilty you are, how you love to be guilty!" (2.5.110). Her accusation, though borne out of anger, might hold some degree of truth. David does seem, to an extent, to be basking in his guilt.
When he comes to decisive turning points in the story, he often confesses to exactly how he felt at the time. The confession has to do with sentiments as much as actions. For example, when David first sleeps with Giovanni, he recalls his sensation as they lay down on the bed: "With everything in me screaming No! yet the sum of me sighed Yes" (2.5.138). After Giovanni confesses to what happened in Italy, David holds him but says, "Something had broken in me to make me so cold and so perfectly still and far away" (2.4.195). The point is that, in each of these key moments in the confession, David sympathizes with his former self instead of condemning it. He is trying to tell what happened, not to judge.
By doing so, David often allows himself to be swept up by the emotions of the past in a wave of nostalgia. Even as he meditates on Giovanni's execution, he says,
I suppose they will come for him early in the morning, perhaps just before dawn, so that the last thing Giovanni will ever see will be that grey, lightless sky over Paris, beneath which we stumbled homeward together so many desperate and drunken mornings. (1.3.198)
When David's thoughts first go up to the sky, it is the grey sky of the morning of Giovanni's execution. Yet when they come back down to earth, his thoughts are of his memories wandering through the streets of Paris with his lover. The story may be a confession, but it is not one that is going to deny the pleasures of the past.