Prior to the onset of hypothermia the body maintains a relatively stable temperature whereby heat production is balanced by heat loss. When the outside environment gets too cold or the body's heat production decreases, hypothermia occurs (hypo=less + thermia=temperature).
The main symptom of poison oak, ivy, or sumac is an intensely itchy, red rash. ... However, you should contact a doctor right away if you are highly sensitive or have the following symptoms: Swelling of the face or throat; Rash on the genitals; ...
As for a red face, this can have a wide variety of causes including rosacea (a skin condition that may also cause swelling and sores), allergies, inflammatory conditions, fever, and sunburn. Medications (including some used to lower blood pressure) can also cause a red face as a side effect. However, one thing that's very unlikely to be behind your red face is high blood pressure. So that's one less thing to get hot and bothered about.