There is no need to panic about cracking your oboe in a pit situation. My middle daughter has been doing it for YEARS and her oboe is crack free. She only worries about being flat for the first few measures.
If the pit is warm enough for you to sit comfortably wearing a dress shirt, it's warm enough for your instrument.
If the pit is warm enough for you to sit comfortably wearing a dress shirt, it's warm enough for your instrument.