DC Voltage Regulation 18V to 12V
With heatsinking, your solution will indeed work. However, bear in mind that the minimum headroom needed by your regulator is 2.2V above the desired output voltage. Once your LiPos discharge below 14.4V, your load circuitry will start to suffer.

Series resistors can help move some of the power out of the regulator but since they introduce a voltage drop will further reduce the available power you can get from the batteries.

A better choice for your application would be a buck-boost converter, which would allow your LiPo to discharge below 12V and continue to provide energy to your load, and would operate much more efficiently than the lossy regulator.

If the end application 'needs' clean DC, you can use the buck-boost to make an intermediate voltage (say 15V) then post-regulate it with a linear regulator - it will cost you efficiency but still allow you to get more energy from the LiPos than a regulator alone.