My initial recommendation would be to not carry the extra weight of a stove and fuel. However, two ideas come to mind:
1. If you are just trying to warm a drink along the path, not anywhere where there is a fire danger, I recommend a folding (flat) metal stove with the hexamine fuel pellets. This combination is markedly lighter than carrying any of the backpacking stoves with a can of fuel. Yes, the round cans or propane fuel or white gas can be bought along the way, in larger towns and cities. There is ample and very good information here (above) about that. But, and IMHO it is heavier and larger than the folding stove with heat tab option.
2. The lightweight thermos idea is brilliant. However, I would compare the combined weight of the empty thermos versus the flat-folding stove and fuel tabs. Also, you should be able to "top off" the thermos at any open cafe or bar, as they all make coffee and tea. I am sure you can "buy" a fillup of hot water too.
As you would be carrying water anyway, I would not include that in the weight comparison. It is a "wash," or "mas o menas" (or or less) as they say...
I hope this helps.