Jupiter doesn't have quite the mass for achieving brown-dwarf status (a star that never managed to light up), but it's not very far away.
I read a theory about the possibility to light up Jupiter with numerous hydrogen bombs deep inside it, should the Sun ever start fading, but I doubt it would be a good idea.
If Jupiter suddenly was lit, the temperature on Terra would increase at first, and then vary as the distance between Jupiter and it changed. During the hot periods, when Jupiter is near, I suspect civilization would only be possible around the polar regions. It would be the end of the world as we know it™!
On the other hand, should the Sun start fading for some reason, It might be a good idea. :-)