I'm hoping someone here can help me with this question...

I know that we know the record highs and record lows for each day, but
do we know the highest low on record for each day, as well as the
lowest high for each day? Here's why I'm asking...

Regarding lows, it usually gets coolest at night, but to me, you
*really* know how cold it was on a particular day by looking at the
high temp for the day. In other words, a day where the low was 0F is
one thing, but a day where the *high* was 0F is something else... in
South Dakota we often reach 0F during the night in the winter, but a
day where you don't get above 0F is something else! And vice versa with
highest lows... if you didn't get colder than 85F, that tells you a lot
more about the day than saying that the high was 80F.

So: are highest lows and lowest highs kept on record? If not, is there
a website that just gives the highs and lows for each day of the year,
going way back?

Thanks!