Possible Clues:

• Very early morning
• 'Each with less than sixty minute parts before 14 down (5,5)'
• Hot, Everyman's wearing lingerie in period after midnight
• 1 a.m. to 3 a.m.
• Time after midnight and before dawn
• I am the first of them
• I am the first of them to give you short time
• Early to go on short time
• I am the first of them to be on short time
• Fewer than sixty minute bits each?