Are AA battery and 18650 battery the same?
An AA cell is not the same as an 18650 cell. 18650 designates lithium-ion batteries of nominal voltage 3.6 Volts each. These typially consist of the actual lithium-ion battery and some circuitry, as shown in this image:

 (source: WikiPedia)

Primary (non-rechargeable) AA cells are typically around 1.5 Volts each, such as the classic Zinc-Carbon batteries, as well as some Alkaline batteries. 
Rechargeable AA cells have nominal voltages that vary with the chemistry: Nickel-Cadmium and Nickel-Metal-Hydride ones are around 1.2 Volts each, Nickel-Zinc are around 1.6 Volts.

In brief: No, the 18650 cells can not be used in place of standard AA batteries, rechargeable or otherwise: The nominal voltage of the 18650 is significantly different from the 1.5x3=4.5V of the three AA cells, assuming those are connected in series. In case the AA cells are connected in parallel to supply sufficient current to heat the element, that's worse, as the voltage of the AAs would be 1.5 volts nominal.