- You may be looking for the similarly-named novel.
The Heart of the TARDIS (also known as space-time element) was a core element of TARDIS technology.
Whether it changed positions like other rooms in the Doctor's TARDIS was unclear, but during the times of the Fifth, Ninth, Tenth and Eleventh Doctors, it was apparently located beneath the central console.
A regular pulse, the heart worked to the keep occupants in the same time frame as their surroundings during materialisation; too slow and the TARDIS would be lost in the past, too fast and it would head into the future. If it suffered problems, such as a skipped beat, the TARDIS would materialise at a point in time to allow for repairs. (AUDIO: 1963)
Commander Maxil removed the space-time element to stop the Fifth Doctor from leaving Gallifrey to avoid his execution. Damon was asked by the Doctor to find a new one, possibly without the recall circuit who let the Time Lords summon the TARDIS on the planet; eventually Damon reassembled and replaced it to allow the Doctor to continue his travels. (TV: Arc of Infinity)
When trying to get Turlough to sabotage the TARDIS, the Black Guardian directed him to the heart of the TARDIS, describing it as a space-time element and ordering him to rip it out. While he could not remove it completely, he tampered with it enough to make the TARDIS begin to break up. It was this tampering that led to Nyssa leaving the TARDIS. (TV: Terminus)
On one occasion, it opened as the TARDIS was being ripped apart after Blon Slitheen had programmed a tribophysical waveform macro-kinetic extrapolator to tap into the greatest power source available, in this case the TARDIS. When Blon Slitheen looked into the Heart, she regressed to a Raxacoricofallapatorian egg, fulfilling her wish for a clean slate. (TV: Boom Town)
On another occasion it was forcibly opened by Rose Tyler, Jackie Tyler and Mickey Smith, who used an attached chain and the pull of a large, yellow tow truck to rip the console apart. (TV: The Parting of the Ways)
When Rose Tyler looked into the Heart, it fulfilled her wish to save the Doctor and infused her with god-like powers. She took the TARDIS to Satellite Five, where she saved the Doctor and destroyed an army of Daleks, including the Emperor. She was also infused with vortex energy. To save her life, the Ninth Doctor took the energy into himself at the cost of his own life. He regenerated into the Tenth Doctor. (TV: The Parting of the Ways)
After the Tenth Doctor's regeneration (TV: The End of Time) caused massive damage to the control room and forced a crash-landing, the console room was repaired and remodelled into a new design. Now the Heart was relocated right below the console, covered by a protective bubble, instead of inside it. The cover also helped hold up the glass floor. (TV: The Eleventh Hour)
When the TARDIS collided with a salvage ship used by Van Baalen Bros., the engine was critically damaged, exploded, and opened a time rift, visually reminiscent to a crack in time, through which the past and future began to leak. The TARDIS managed to freeze the explosion in time, but the Doctor stated that it was merely a temporary fix. The explosion was later prevented when the Doctor used a magno-grab remote to prevent the collision and negate the timeline preventing it from happening. (TV: Journey to the Centre of the TARDIS)