No, but when second growth or plantation forests are cut down for heating/electricity it puts pressure on more mature forests for timber products, wood pulp, etc. The plantations/farmed forests could be instead used for these products.
You can use managed forests for those too. This isn't an either/or problem.
Deforestation is bad, but it doesn't happen because people want timber. Deforestation happens because people want to use that land for something other than growing trees, the most common reason being to make room for cattle pasture.
If you want to save the trees, don't stop burning wood, almost all wood products available today come from sustainably farmed managed forests. If you want to save the trees, stop eating beef. Also palm oil.
Fuel wood comes from farmed forests that re-plant every tree they take down to recycle the forest every 25-30 years.