Its because she was focusing the flames on Claire. The heat was removing the oxygen from Claire in the immediate sense not fully, that is why she brought up the idea of Water Boarding where the prisoner feels as if they are going to drown even though there is no threat. She made Claire think she was sufficating even though there was no danger not because of her ability but also because if you watch the episode again you'll see the storage container changing from dark to red move towards Claire and immediately change from fiery red and follow Claire along with the flames in her hand. If she were actually removing the oxygen completely, she would have fainted before Claire. It was to show that not all fighting is physical but like Sylar many of the villains will fight psychologically and it can be as physically damaging as a straight forward attack. The Storage Container was increasing in temperature because the "sizzle" when Claire touched it but if it were hot enough to really cause damage it would have burned off the skin of her hands when she touched it, she wouldn't have felt it but it would have stopped her from escaping immediately. It was getting hot to increase the feeling of temperature because she would sweat along with the immediate oxygen burn made the mindgame that much worse.
Many ask how she could teach Claire how to fight when she is a firestarter.....she taught her a really valuable lesson that the mindgame is more important than the direct fight. Think about the preview where she has the scalpel with Peter in the future scenario. He can feel pain but cannot die because he can mimic her powers, which means any repeated damage would take a mental toll more than a physical one.
Excellent question.