Alright, what the hell, here's my guess:

Volume of each cigar (assuming box pressed to make a nice square cigar)
((50/64)*(50/64)*5) =3.051758 cubic inches

Divide by 12 to get cubic feet multiplied by 150 sticks
(3.051758)/(12)*(150) = 38.14697 cubic feet of cigars

Multiply by the Heat Release of 250 BTU's per cubic foot
(38.146397)*(250) = 9536.743 BTU's

It takes .02 BTU's to raise 1 cubic feet of air 1 degree in one hour, but I don't really know the entire volume of the room, but we're not trying to raise the temperature in the entire room, just enough of a raise to activate the heat detector. So, since the detector is 2 feet from the centerline of the fire, I will assume a volume of 4*4*10 to account for heat loss to the sides or a total room volume of 160.

1 BTU/hr x 160 ft3 = (50/160)o F/hr = 0.3125o F/hr
(9536.743 BTU/hr)*(160 ft3) = (9536.743)*(0.3125)o F/hr = 2980.232o F/hr

The starting room temp is 75 and the detector will go off at 125, so the temp needs to be raised 60 degrees.

60 / (2980.232o F/hr) = .020133 hours, or 1.2 minutes.

Sheesh. All this for some crappy, pre-lit & tequila smoked sticks???

Congrats on passing Buzz!