It depends on what you mean. For example, just pulling the air and smoke with a vacuum would cause fresh air with more oxygen to flow into the fire. With more oxygen, the fire could burn hotter. On the other hand, if you made the fuel just right so that no smoke is made, then the fire could burn hotter as it uses up the fuel more efficiently.
However, just putting some rocks around the fire will make it feel hotter, as the heat goes into the rocks which spread out the heat more comfortably. A fireplace is designed for this.
However, every fuel has a maximum temperature. No amount of pulling smoke, or flowing oxygen, or carefully placed surroundings will make pine logs burn at the temperature of the sun! This is why coal burning forges exist. Folks who heat up metal and beat it with a hammer have some detailed opinions on exactly which kind of coal is hottest.
To directly answer the question, yes. Just about every way I can think of pulling the smoke out could make the fire burn hotter, but there is no guarantee that the measured temperature would increase because there are other things that make a big difference.
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