Does the interior temperature of the vagina increase, when a woman is
menstruating? If so how much?

Hi clakat,

The change you are describing is called the Basal Body Temperature
measurement.  As the female body as a whole goes through changes on a
monthly cycle, one aspect of this is the internal body temperature,
which varies cyclically as well.

"Your basal body temperature (BBT)- This is the temperature of your
body at rest. Your temperature is affected by the time of day,
physical activity and eating, drinking or smoking. In order to be
accurate, you must take your temperature, using a special basal body
thermometer, every morning just after you've woken up and before
you've gotten out of bed. Around the time of ovulation, the BBT will
rise approximately 0.2-0.4 degrees Fahrenheit, and stay at
approximately that level until menstruation."
[ http://www.allwomens.org/services/fert.htm ]

Note that this temperature change is effective for the entire body,
not just a localized change in the vagina.  Basal temperature can be
taken at any place that body temperature is usually taken- the vagina
is just one particular (and fine) orifice for this test.  More details
about how to take these measurements can be found at:
[ http://www.fertilityplus.org/faq/bbt/bbtfaq.html ]

So, yes, the interior temperature of the vagina does increase during
the menstrual cycle.  However, during the few days of menstruation,
the temperature actually DECREASES.  This can be seen on the chart at
[ http://anatomy.med.unsw.edu.au/cbl/embryo/wwwhuman/MCycle/MCycle.htm
]

This is because the internal temperature makes a jump UP when
ovulation occurs, which occurs around the day-14 point of the cycle. 
It then remains relatively high until just before day one, when the
woman gets her period.

As for how much the temperature fluctuates, different gave different
numbers, but they were all in the same ballpark.  The chart at
[ http://anatomy.med.unsw.edu.au/cbl/embryo/wwwhuman/MCycle/MCycle.htm
]
from the University of New South Wales Medical School says a change of
0.5 degrees celsius can be observed.

AllWomens.org says that 
"Around the time of ovulation, the BBT will rise approximately 0.2-0.4
degrees Fahrenheit, and stay at approximately that level until
menstruation."
[ http://www.allwomens.org/services/fert.htm ]

Fertilityplus.org states:
" The average range of BBTs is between 97.0-97.7 before ovulation and
97.7-99.0 after ovulation. Ideally, a woman’s temperature will not
bounce around more than .5 degrees in the follicular phase and will
stay above the coverline during the luteal phase. "
[ http://www.fertilityplus.org/faq/bbt/bbtfaq.html ]

Please remember that Answers and comments provided on Google Answers
are general information, and are not intended to substitute for
informed professional medical, psychiatric, psychological, tax, legal,
investment, accounting, or other professional advice.

Therefore, please speak to a doctor if you are thinking aobut using
basal temperature as a method for birth control or increasing the
chances of pregnancy.

I hope this information has prooved satisfactory.  If necessary,
please ask for a clarification before rating this answer.  Thank you
for bringing your question to us!

Sincerely,
Andrewxmp

Search terms used:
vaginal temperature menstrual

Thank you that answered my question perfectly.