Yes, excessive higher alcohols can be caused by warm fermentation. What matters is the temperature of the fermenting beer and not the ambient temperature. At 66 F ambient, an active fermentation can easily raise the beer temperature into the low 70s. Coupled with a strain that is prone to producing lots of higher alcohols you'll end up with this hot alcohol tatste.
The good thing is that it will age out.
For your future beers I suggest placing them at least in a tub of water. The larger thermal mass will limit the rise in temperature.
It's only the temperature during active fermentation that matters for fusel and ester production. Towards the end of the fermentation the yeast doesn't grow anymore and doesn't consume amino acids. As a result the pathways that lead to esters and fusels are not active anymore.