I have that canteen, but never tried tried to use the cup over a stove/fire just yet - but I don't see an issue. Its my edc to work, and a perfect size to be sitting on my desk. As a side note: it does look a bit like a flask, and can't tell you how many times people ask what spirits I have in it!
I even emailed customer support to find out what kind of metal the cup is, and if they recommend such a task... They kept mentioning the steel in the canteen (stainless steel and now aluminum oval bottles). I couldn't get an answer to my question, so I gave up.
Sorry, No help... But it is a cool product.
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"One should not increase, beyond what is necessary, the number of entities required to explain anything"
William of Ockham (1285-1349)