Expanding on 25362's last response, consider a column in which only a tiny fraction of the feed is removed overhead, and nearly all of the feed out the bottom. To achieve a certain degree of stripping of light stuff from the bottoms, a certain boilup is required, depending on the relative volatility of the light stuff w.r.t. the heavy key(s). Except for any vapor knocked down at the feed tray by a cold feed, the vapor will run up the top section to the condenser. If only a tiny bit of material is withdrawn as distillate, then the top section L/V will be very close to 1.0 (total reflux), and increasing the vapor coming up (by means of hotter/vaporized feed) will have almost no effect on the rectification. Meanwhile, the stripping section still needs the same L/V (or V/B) to do its job, and adding heat to the feed has no effect there either; extra feed turned into vapor just gets condensed and returned to the top of the stripping section as liquid again, so the liquid running down the rectification trays and the boilup stay about the same.
For the reverse situation, with a tiny bottoms stream (say, a residue of some sort), the reasoning is similar, except that the stripping section is near total reflux, and adding heat to the feed means that much less heat needed at the reboiler to provide vapor entering the rectification section. As you move from the situation of tiny distillate to tiny bottoms, adding heat to the feed does make increasingly more difference, which may be beneficial or not, depending on the situation.
A quick series of runs on any decent process simulator will quantify the changes to duties and traffic in the column as you add heat to the feed, but understanding the extreme situations helps make sense of what the simulation is telling you.