Answer and Explanation:
The line "My heart grew sick; it was the dampness of the catacombs that made it so," appears in the final paragraph of the short story "The Cask of Amontillado", by Edgar Allan Poe. The one saying it is the narrator and main character, Montresor, who was at the moment "burying" his friend alive. The line reveals the Montresor's heart is not sick due to what he is doing. That is, he does not feel any remorse for torturing his friend this way. It is the dampness of the catacombs that's making him feel sick.
Throughout the story, Montresor's actions and words show he has calculated every single step of this tragedy. He is indeed a cold man. At the very first paragraph, he shows resolution, anger, and desire for revenge:
At length I would be avenged; this was a point definitely, settled --but the very definitiveness with which it was resolved precluded the idea of risk. I must not only punish but punish with impunity.
The line we are analyzing here completes the lines above, the ending of the story matching its beginning. Montresor has already made his decision. His heart does not waver for a second.
