Now in your case I see two directions to troubleshoot your problem:

1) Check the batteries impedance.

2) Check the current drain of the engine.

1) Some recent charger like the new Graupner Ultra duo plus 30 will tell you the discharge and charge impedance of the batteries. This is also a good parameter to monitor the health of the battery on the long run ( battery log required ).
Note that a lipo battery with a normal impedance level will never catch fire spontaneously. So it is also a good safety tool.
If you don't have such a tool in your workshop, you will have to monitor the battery voltage under discharge condition and see if it remains constant.

2) Since your engine is working normally on gas, you can suspect an abnormal heater condition. Check the current drain during the preheat phase. Anything largely above 15 amps is not normal. You'll need a hall effect amp meter preferably for this job.
Note that the next phase ( preheat 2 + starter clutching in ) will drain up to 30 amps burst during starter engagement. Once again, most modern healthy Lipo bateries will handle this without dropping the voltage.