^to be fair Ulfrics character isnt "hot headed" as much as motivated, im assuming your talking about the tone of his voice in his speeches because thats the only sign i could draw to being hot headed, even so i would say hes just getting his men pumped for battle more then anything else, when you talk to him alone hes actually very calm and collected.
also the Empire is weakened as it is so even without a Civil War they probly dont stand a chance against the Dominion at this point, if the Thalmor believed the Empire would rebuild and would have become so powerful in 30 years to threaten them they would have destroyed what was left of the Empire back in the War instead of letting it rebuild. Do i think the Nords should completely cut ties with the Empire? no, thats a stupid move. Should the Empire recognize Skyrims independance? yes. you gain Ulfric, whos a much more seasoned ruler than that Elsif who cant govern to save her life, and someone who faught the Thalmore and was even one of their agents in Skyrim prior to giving them the finger and stopped taking orders.