Is watching the heart beat (instead of watching the breath) a known form of meditation?

The Wings to Awakening by Thanissaro Bhikkhu, on page 83 says,

There is the case where a monk—having gone to the wilderness, to the foot of a tree, or to an empty building—sits down folding his legs crosswise, holding his body erect and setting mindfulness to the fore [parimukham: in the Abhidhamma, this is translated literally as “around the mouth”; in the Vinaya, the same term is used to mean the front of the chest]. Always mindful, he breathes in; mindful he breathes out.

See also What is the Interpretation of Parimukham in the context of Buddhist Meditation?.

According to the above the heart area seams to be a valid focal point. Thanissaro Bhikkhu / Achan Lee also mentions about other focal points. (See: With Each & Every Breath and Keeping the Breath in Mind.)

Having said this I would advocate how S.N.Goenka advices to keep the focus.

1. For a beginner - the triangular area from top of your nose to the base. This includes the inner walls of the nostrils where some feel the breath.
2. As you advance in concentration - the triangular area from the tip of the nose to the base (the upper lip). This includes the tip of the nose and the sides, the nasal bridge and the base or simply around the nostrils and upper lip.
3. As you advance further - the base of the nose (upper lip)
4. As you advance even further - the centre of the upper lip (Philtrum). This point is referred as the spot in the chapter "Keep Your Mind on the Spot" (p 72 as per table of content in the original book but p 54 in the linked PDF as it looks like and extract) in The Way of Ultimate Calm by Webu Sayadaw.

And in terms of what you should perceive as the breath (Anapana Sanna):

1. Beginner - Flow of perspiration
2. Intermediate - Touch or brushing of the flow of perspiration
3. Advance - the 4 elements associated with the breath (gaseous nature of the flowing air, heat or difference in heat of the in and out breath, solidity of the the point of focus, and moisture in the out breath and nose. [gross level] Also the same properties in every sensation you experience. [Subtle level] Further you can look at the Space Element initially bodily cavities like the nostrils [gross] and much later the gaps between the arising and passing of the Kalapas [subtle] and also Consciousness Element which in short is the recognising of arising and passing of contact and sensations again initially at a gross level where you recognise the start of a pain or sensation and the end of it in terms of time and also the location in the body where you start from boundary of the pain to the centre where it is the most intense [gross] and more subtle level when you start seeing the Kalapas which make the sensation. For further details see: Dhātu Vibhaṅga Sutta, Titth’Ayatana Sutta, Maha Rahul’ovada Sutta, Maha Hatthi,padapama Sutta, etc.)
4. In preparation to switching to Sathipattana - sensations associated with the focal point and the perspiration process

When ever you find some combination difficult you can switch combinations like say the pure sensation at a focal point than the flow of respiration. If you feel dull and your mind is less sensitive you can increase the areas.

It is both right and wrong to say either you should regulate the breath and / or you should not regulate the breath! You should direct your sustained attention to the breath with the intention (but not necessary the direct action or direct manipulation of the respiratory process - if you manipulate the breath this becomes like Pranayama, hence I would generally say do not regulate the breath as this advice is less prone to mistakes by the novice) to clam your breath. Traditionally 4 steps are recommended:

1. Concern - Abhoga
2. Reaction - Samnnahara
3. Attention - Manasikara
4. Reviewing - Paccavekkhana

(See Knowing and Seeing - Revised Edition by Ven. Pa Auk Sayadaw p 45 for further explanation)

In simple terms this is keeping the though in the back of your mind that the breath should calm where you focus actively to keep your mind on the breath and whether it is long or short, smooth or not, etc.