Two things:

First, distilled water (at least if you buy it off the store shelf)
usually is not pH 7. It reacts with CO2 in the air and becomes
somewhere between 5.6 and 7.0 from what I've read. Tested some from a
freshly opened jug here at work once and it was a ways from neutral -
don't remember the measurements now.

I guess it could be easily adjusted to 7, but would this affect the Ta
reading?

Second, shouldn't your pH have went up after boiling, Bill?