I do not know if a 10 watt heater will work or not.. But I do know this.
In many markets (Google Botique gas) the gasoline sold in January, and July, is different,, The stuff sold in July has additives that make it harder to vaporize..
SO if you have July gas, and well today it's February (Still January season) often the thing will not start at all.
The solution is to make sure it's full of "Winter Gasoline" which has a lower vapor point (boiling point) and more easily turns from Liquid to GAS (GAS here refers to a statge of matter, vapor not liquid) so the Generator can burn it.
I have actually verified this with a different make of portable,, Would not start till warmed.