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Ken,
There are so many variables, some of which are very sensitive, and / or can vary over a wide range of plausible values, so I would be cautious about using the following other than as a very indicative guide.
However, for what it's worth, if I assume a "worst-case" convection coefficient of 5 W/m2.K on both sides of the paper (representing still air), my thermal analysis suggests the 15 mm hot-spot will reach an equilibrium temperature of 550K (277 Celsius) with an input heat flux of 13,300 W/m2, and about 600K (327 Celsius) with a heat flux of about 16,600 W/m2.
In practical terms - less than about 10,000 W/m2 (10 kW/m2) applied to a small area of paper SHOULD be low enough to avoid ignition; anything over about 12 kW/m2 would run the risk of ignition.
Take this all with a generous handful of salt - it will be interesting to see how these predictions stack up against some actual testing!
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