Sometimes "God" alone refers to the whole Trinity, but sometimes it refers to only the Son, and times only the Holy Spirit.
Here it cannot be the whole Trinity because the Son is not a spirit. Scripture is just as clear that the Father is also not a spirit.
Clearly that is a figure of speech. spirit of God doesn't need to be in out pumping hearts. Heart is usually meant as mind where our love and feels originate from. He is symbolically there in Christians. Christ is a physical being in a glorified humanoid looking body. He ate human food and could be touched. Something that is pure spirit is not like that at all and that is the nature of Holy Spirit and all spirits.