Jupiter cannot turn into a star because it does not have enough mass. Stars form from the collapse of large clouds of gas and dust, and the minimum mass required for a cloud to collapse and form a star is about 8% of the mass of the Sun. Jupiter is only about 0.1% the mass of the Sun, so it is far too small to ever become a star.

However, Jupiter is a gas giant planet, and it does emit heat. This heat is generated by the gravitational compression of Jupiter's massive interior, and it is emitted as infrared radiation. Jupiter radiates about twice as much heat as it absorbs from the Sun, so it is actually a net heat source for the Solar System.

If Jupiter were to gain enough mass, it would eventually reach the critical mass for fusion and become a star. However, it is very unlikely that Jupiter will ever gain enough mass to become a star. The most likely scenario is that Jupiter will remain a gas giant planet for the rest of its life.