Without digging too deep, and witout actually looking at the file... the default pyro2 shader seems to require a density (smoke) volume to render anything. I am currently unsure why it's set up this way, but this seems to be the case.
One workaround is to remap the smoke density target range.
In the simulation, turn "emit smoke" back on.
In the pyro2 shader, under the "smoke" - > "Density" tabs, under "field shape" enable the "fit to range" toggle.
Set the "target range" to go from 0 -> 0 rather than 0 -> 1.
Your fire should now render without smoke.
Hope that helps.
-=X