B737 Captain was informed during climb that an oven came on uncommanded. The Flight Attendant was instructed to pull the associated oven circuit breakers with no effect. Circuit breakers for both ovens were then pulled with the desired effect and flight continued to destination.

Narrative

The Flight Attendant called us up on the interphone (during climb) and stated that there was a problem with the forward oven. She said it came on uncommanded. She opened it up and smelt some fumes but said there was no smoke or fire. I instructed her to pull the circuit breaker for the right (affected oven). A little while later she said the oven was still getting hot so I turned off the cab/utility switch momentarily. Maintenance was contacted. They advised for to pull both circuit breakers just in case and that I should not have to turn off the cabin/utility switch. The Flight Attendant pulled both breakers and I turned the cab/utility switch back on. A little while later the Flight Attendant called back up and said it was still getting hot so at that point I went back to check. I found the oven warm but not powered up. It continued to cool and all involved (Maintenance; all four Flight Attendant's; and the First Officer and I) were in agreement that it was safe to continue. About the last forty five minutes of the flight; the other Flight Attendant said that her throat was getting a little scratchy. She also stated that they both had a slight headache. I asked if they were dizzy; sick to their stomach; etc. and they said no. I asked if they wanted to contact med-link or have the paramedics meet the plane and they initially declined. Later though they agreed to have the paramedics meet the plane. Dispatch was contacted and med-link was notified. The paramedics met the airplane and they were examined and advised them to go to the hospital.