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. You may further increase the pain-reducing benefits of exercising by "earthing" yourself (creating barefoot contact with the ground).2
Walking barefoot through newly fallen snow
This toothache remedy anecdotally reported by famous naturopath Sebastian Kneipp combines at least two approaches against toothache - exercise and earthing2 (as well as possibly some placebo). In his classic "My Water Cure"3, Father Kneipp tells the story of a girl of seventeen with extreme toothache whom he advised to walk through the newly fallen snow for five minutes since her toothache would soon vanish if she did. Ten minutes later she returned from the garden and exclaimed that her toothache had gone. (Kneipp adds that barefoot snow-walking must only be done when the whole body is perfectly warm, and never by people with perspiring feet, wounded feet, or open or suppurating chilblains.)
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.
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."
2 For some background on earthing see Bruxism & TMJ pain suggested nontoxic cures & natural remedies: Earthing / Grounding.