Is it permissible to place one's hand on the heart when mentioning the Prophet (peace be upon him) or one of the righteous, out of respect and to express love, or is this act considered an innovation (bid'ah)?

What is prescribed when the Prophet, peace and blessings be upon him, is mentioned is to send blessings upon him. As for placing the hand on the chest or head when he is mentioned, there is no legal basis for it. Persistent adherence to this practice may lead people to mistakenly believe it is part of the Sharia (definition), and this falls under the category of innovations (bid'ah) that begin without the intention of worship but then spread until they are mistaken for Sunnah (definition). Ibn Mas'ud warned against this temptation. It has not been narrated that the Companions did this, and all good lies in following those who have preceded us.