No, the fire is extinguished.
Korgazhar
The Keeper’s axe is giant-sized, so you would be at a disadvantage wielding it.
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STR check - (1d20+2)
(1) + 2 = 3
Toll the Dead(Damage) - (2d12)
(68) = 14
Scorching Ray (3 beams) ranged spell attacks, damage - (1d20+7, 1d20+7, 1d20+7, 2d6, 2d6, 2d6)
1d20+7 : (9) + 7 = 16
1d20+7 : (16) + 7 = 23
1d20+7 : (3) + 7 = 10
2d6 : (43) = 7
2d6 : (32) = 5
2d6 : (15) = 6
Insightful Fighting on fire giant - (1d20+2)
(3) + 2 = 5
Fire Giant Deception - (1d20+1)
(8) + 1 = 9
Attack, Extra Attack, Bonus attack (PAM) - (1d20+11, 1d20+11, 1d20+11)
1d20+11 : (17) + 11 = 28
1d20+11 : (6) + 11 = 17
1d20+11 : (15) + 11 = 26
Damage (attack, extra and PAM) - (1d10+7, 1d10+7, 1d4+7, RA)
1d10+7 : (101010107) + 7 = 54
1d10+7 : (2) + 7 = 9
1d4+7 : (4443) + 7 = 22
GWF Reroll - (1d10+7, RA)
(5) + 7 = 12
Attack, weapon, fire, sneak - (1d20+9, 1D8+5, 2d6, 3d6)
1d20+9 : (1) + 9 = 10
1D8+5 : (3) + 5 = 8
2d6 : (31) = 4
3d6 : (243) = 9
Extra attack,damage,fire,sneak - (1d20+9, 1d8+5, 2d6, 3d6)
1d20+9 : (10) + 9 = 19
1d8+5 : (8) + 5 = 13
2d6 : (66) = 12
3d6 : (265) = 13