I'd give your character a minute at best.
Problem 1: oxygen
Contrary to depictions of Pinocchio, a creatures stomach is not filled with breathable air. The stomach contracts regularily in order to store the food in as little volume as possible. In fact, trapped air is regularily expelled as burps. Your character would survive as long as he could hold his breath.
Problem 2: swallowed debris
Let's assume the whale swallowed not only a man within his log cabin, but also a bubble of breathable air. The stomach contracts and moves in order to mix its content with stomach acid to aid digestion. That means, massive logs and other debries are constantly moved around, most likely crushing or otherwise injuring the man. At the very least they would hinder him from keeping his head in the air pocket.
Problem 3: Stomach acid and panic
Now let's assume the man was swallowed with a breathable air pocket but without debries. He would now swim in one of the strongest naturally occuring acids, in complete darkness. Realisticly he would have gotten the stuff into his eyes and probably lungs as well, causing coughing, burning pain in the eyes and panic. It's damn hard to tell up and down in complete darkness, causing more panic. If the creature is so big that he has to swim, he would swim in the slimy, viscous contents of a stomach which would tire him out quickly. Even if he keeps his eyes and airways free of the acid, he would start to feel burning pain all over his body really soon. Eventually either he gets some of the acid into his airways and suffocates, looses conciousness because of the pain or simply tires out and drowns in acid.