I assume, but am not sure, that this is caused by someone else in the house competing with the shower for cold water.
I'm guessing an anti-scald valve might be necessary but perhaps there is a way to keep the cold water pressure higher so that it doesn't drop as much when someone flushes a toilet or something. The shower in question is on the 3rd floor.
Added: I have since learned of at least three approaches. 1) pressure balanced valve 2) thermostatic mixing 3) anti-scald shower head
Here is a good site comparing the first two: http://www.hometips.com/buying-guides/shower-valve-anti-scald.html
The anti-scald showerheads I have found online are very inexpensive (under $30) but poorly reviewed.