After a root canal&crown, I am experiencing pain (on/off)and sensitivity to hot & cold. Will I need an extraction now? Dentist is also out for 6 days.

Dentist can examine. Each root canal and crown varies in how long it lasts. If symptoms show up, the dentist will have to re-examine it before deciding on what to do next. If the dentist is out of town, and a person is in lots of pain, he can see his primary care doctor or go to the er. After his dentist returns, they can together decide about extraction, implant, etc...
Unlikely. These symptoms are not normal after root canal treatment, the cause of which may be for a wide variety of factors. I encourage you to have your treating dentist or an endodontist specialist to address these symptoms you are experiencing.
See the dentist. You should not be having hot or cold sensitivity after a root canal has been done...See your dentist as soon as possible to rule out another tooth or another canal in the tooth.
See someone. If your dentist is out for 6 days, hopefully they have an emergency number for you to see another dentist who is covering the office. Don't hesitate.