Toothache relief
Exercise and increasing blood circulation and lymph flow
It can be speculated that increasing blood and lymph flow and circulation via various routines works against toothache both by helping to decongest the affected area (see excerpts on causes of dental pain from "Dentistry and Its Victims") and by allowing the tooth/gum to be better supplied with nutrition and oxygen while being drained of toxins more quickly.
Exercising in fresh air against dental pain
A friend told me that when he had a terrible toothache, moving (going out and riding his bike) made the pain less severe. An even more powerful effect has been reported by a woman who says that she "jogs away" any illness such as stomach pain or toothache by going jogging in the woods.
Increasing blood flow to head and mouth
Hanging my head down as far as possible helped relieve me from the pain of a very bad toothache, temporarily stopping it (it resumed after I straightened myself). Another friend reported that chewing gum improved his toothache.
Hot wet washcloth/warm water bottle
Repeatedly applying a hot wet washcloth to the aching spots reportedly works for extreme toothache pain.
Similarly, a bag or bottle filled with warm water can be held against the sore area.
Someone reported success with taking a dish towel, slightly wetting it and throwing it in the microwave1 for c. thirty seconds. After putting it against your face, the heat may put you to sleep.
It's possible that only toothaches which are not caused by infection can be alleviated with moist heat applications, while those involving infection rather respond to cold treatments, see Simply numbing toothaches: Cold & Ice.
Alternating hot and cold applications / rinses
The following technique using two cloths strongly relieved someone's terrible toothache: she heated one cloth up and cooled the other one. She then held the hot cloth close to the aching tooth, swapped to the cold one, then reapplied the hot etc.This should also be doable using water-filled bottles etc.
A variation using hot and cold water gave someone else great relief, quote, "It really worked!!! My toothache was horrible! The hole right side of my face felt swollen and in pain. It was so painful I could not hold my tears in, or sometimes even sleep... I rinsed my mouth with very hot (as hot as I could actually stand) water... And then right away I rinsed with cold water. It worked. I am amazed."
1 For reasons of health concerns, Healing Teeth Naturally does not endorse microwave cooking.