Hadiths Concerning the Presence of Heart
There are many hadiths from the infallible and pure Ahlul Bayt (A.S.) concerning urging the "presence of heart". It suffices to translate some texts of those narratives:
The Messenger of Allah (S.A.W.) is quoted to have said: "Worship Allah as if you see Him. If you do not see Him, He does see you." 
From this noble hadith two of the degrees of the presence of heart can be realized:
The first is that the salik discerns the Beauty of the Beautiful, and is absorbed in the manifestations of the Beloved [hadrat-i-mahbub] such that all the ears of his heart will be closed to all other creatures, while the eye of his insight opens to the pure Beauty of the Lord of Majesty, discerning nothing else. That is, he is engaged in the Present [hadir], neglecting the presence [hudur] and company [mahdar].
The second degree, which is lower in rank, is that the salik sees himself present in His Presence [mahdar] and observes the discipline of the Presence [hudur] and Company [mahdar]. The Messenger of Allah (S.A.W.) says: "If you can be of those who are in the first degree, then worship Allah accordingly, or else, do not neglect the fact that you are in the Presence [mahdar] of the Lord."
Naturally, there is a discipline for being in the Presence [mahdar] of Allah which should not be neglected in respect of the state of servitude. In a hadith, Abu Hamzah ath-Thamali narrates: "I saw Ali ibn al-Husayn (A.S.) performing his salat. His cloak slipped off his shoulders, but he did not try to rearrange it until he finished the salat. When I asked him about that, he said: 'Woe unto you! Do you know at whose service I was?'" 
The Messenger of Allah (S.A.W.) was quoted to have said: "Two of my Ummah stand for the salat, and, although their ruku' and sujud are the same, the difference between the two salats is like that which is between the earth and the sky." 
He also said: "Is the person who turns his face in the salat not afraid that it may turn into the face of an ass?" 
He further said: "Whoever performs a 2-rak'at salat without paying attention to any worldly matter, Allah, the Exalted, will forgive him his sins. 
In another hadith he said: "A salat, half of it may be accepted, or one-third, or a quarter, or one-fifth, or even one-tenth. Another salat may be folded, like an old dress, and be thrown back at the face of its owner". "No part of the salat is yours except that part which you perform with an attentive heart." 
Imam al-Baqir (A.S.) has quoted the Messenger of Allah (S.A.W.) as saying: "When a believing servant stands for the salat, Allah, the Exalted, looks at him (or he said: He turns to him) until he finishes, and mercy shadows over his head, the angels surround him from all sides up to the horizon of the heaven, and Allah assigns an angel to stand at his head, saying: '0 musalli, if you know who is looking at you, and to whom you are supplicating, you will look to nowhere, nor will you leave your position.'" 
Imam as Sadiq (A.S.) is quoted to have said: "Eagerness and fear will not get together in a heart unless Paradise is his. So, when you perform your salat, turn with your heart to Allah, the Glorified, the Almighty, because there would be no believing servant who would turn with his heart to Allah, the Exalted, during the salat and invocation, unless Allah would turn to him the hearts of the believers, and with their love He would back him and lead him to Paradise." 
It is narrated that Imams al-Baqir and as Sadiq (A.S.) said: "Nothing of your salat is yours except that which you did with an attentive heart. So, if one performed it completely mistaken, or neglected its disciplines, it would be folded and thrown back at its owner's face." 
Imam Baqirul 'Ulum ( the cleaver of knowledge) (A.S.) is quoted to have said: "of a servant's salat ascends half, one-third, one-fourth or one-fifth to his account. That is, of his salat will not ascend except that part which is performed with an attentive heart. We have been commanded to perform the nafilah so as to make up for the shortcomings of the obligatory salats." 
Imam as Sadiq (A.S.) is quoted to have said: " when you wear the ihram for the salat (i.e. when you prepared for the salat), pay attention to it, because when you pay attention to it, Allah will pay attention to you. If you do not care for it, Allah will not care for you. So, sometimes, does not ascend of the salat except one-third, one-fourth or one-sixth, according to the amount of attention the musalli pays to it. Allah grants nothing to the negligent." 
The Messenger of Allah (S.A.W.) is quoted to have said to Abu Dharr: "Two moderate rak'ats of salat with contemplation are better than worshipping a whole night with a negligent heart."
The hadiths on this are many, but those which have been related are enough for those whose hearts are awake and attentive.
. Biharul Anwar, vol. 74, p. 74, "Book of Ar-Raudah". ch. 4, hadith 3. Makarimul Akhlaq, p. 459.
. Wasa 'il ush-Shi'ah, vol. 4, p. 688, "Book of as salat", chs. on "The Acts of as salat", ch. 3, hadith 6.
. Biharul Anwar, vol. 81, p. 249, "Book of as Salat", ch. 16, hadith 41.
. Mustadrakul Wasail, "Book of as Salat", chs. on "The Acts of the salat", ch. 2, hadith 20.
. Ibid. hadith 13.
. Biharul Anwar, vol. 81, p. 260, "Book of as Salat", ch. 16, hadith 59.
. Mustadrakul Wasa'il, "Book of as Salat," chs. on "The Acts of the Salat", ch. 2, hadith 22.
. Wasa'ilush-Shi'ah, vol. 4, p. 687, "Book of as Salat", chs. on "The Acts of the Salat", ch. 3, hadith 3.
. Ibid., hadith 1.
. 'Ilalush-Shara'i', vol. 2, p. 327, ch. 22, hadith 2.
. Mustadrakul Wasa'il, "Book of as Salat", chs. on "The Acts of the Salat", ch. 3, hadith 7.