I´m trying to customize my heatmap, all looks fine except for one particular detail: the column dendrogram overlaps due to the big amount of columns. Here an example:

I tried to change the width of my plot, however, I had no success. Is there a way to separate more the space between lines in the dendrogram? I´m using pheatmap to do that plot.

You won't be able to 'fix' that without changing the width to something huge, at which time the usefulness will have been reduced quite a bit. You could do something like

png("massiveheatmapwow.png", width = 20000, height = 20000)
print(pheatmap(<arguments go here>))
dev.off()

But unless you are planning to mount that on a wall, it's just too big to be useful. I am not sure why you care that the lines overlap though. Can't you get the gist of the situation from the plot you already showed us? Seems OK to me.