According to the specification, it's 1.2V/240mA = 5 ohms. The nominal series resistor would be 10.8V/240mA = 45 ohms respectively.
Yes, the nature of a series circuit. A switch mode converter would be the only way to get away with less.
I didn't yet talk about power. My math says 2.6W.
In a datasheet, I see the heater current specifications 230mA min, 255mA typical, 280 mA max. So you'll better select the resistor empirically between 39 and 47 ohms or use a rheostat.