I've seen this several times on the forums here. People see a 1250 or 1500 mAh flat cell the size of a book of matches in a cell phone and think they've found an ideal e-cig battery.
Cell phone batteries are no good for an e-cig. For one, they do not necessarily have protection built into them since that may handled by the phone itself. They are just as hazardous as any other Li-Ion cell without it.
The reason cell phone batts have such high capacity for their size is they are designed only for the current drain the particular phone they fit demands. That's usually only a few tenths of an Amp. That's how it is with Li-Ion batteries, the higher the drain capability, the bigger they are or the less charge capacity they have. There is no miracle battery that small with capacity that high and drain limits high enough for an atomizer, at least as of yet.
It's your prerogative if you want to risk it, but cell phone batteries are seriously over-loaded when powering an atomizer. Camera batteries may be okay, but you for sure want to know their drain limit and you need to add a properly rated protection PCB.
BTW, It's not unusual for me to use as much as 250mAh per hour so big capacity for me would be a couple 18650s which is more like 5000mAh.