Washed yeast character carry over?

So I made my first attempt at washing yeast a few months back. It was from some US-05, so if it doesn't work well, not a big deal. Problem was, I had issues with temp control and fermentation occured at 76-78 degrees. The beer has a slight fusel kick at the end, not that bad, but not desired. Since the yeast propogated at these temps, will reusing this yeast cause problems or will I be fine as long as I am below 72 degrees on the next batch I use it for?

My thought would be that it will be fine, cause the fusel is produced by the temp the yeast are consuming the sugar, but I am not yeast expert.

Well, if you rinsed the yeast and they have been dormant for a few months, you are going to want to build a starter for them. Not every yeast cell that went into the jar/bag/whatever you used has survived the rest. If you rebuild the population from the viable cells and repitch a healthy amount of cells into a properly tempered wort, you will not receive the off-flavors associated with the inital fermentation.