Both the mind and the heart possess an "inner eye." On Shabbat the inner eye of the mind opens to see Godliness in contemplative meditation. In the Temple the inner eye of the heart opens to see Godliness in heartfelt prayer.
The verse says, "And they shall make for Me a sanctuary and I shall dwell in their midst," and the sages interpret, "It does not say 'in its midst' [implying that the Divine Presence shall dwell in the midst of the physical sanctuary alone] but rather 'in their midst' – in the innermost point of the heart of every Jew."
Although a non-Jew is forbidden to keep (observe all the laws of) Shabbat, the Temple is meant to be "a house of prayer for all nations." When a non-Jew comes to the Holy Temple in Jerusalem to pour out his heart to the God of Israel in prayer, he experiences the Divine Presence residing in the Temple. The awesome experience of entering God's sanctuary brought many non-Jews (even those who just came to 'pay a visit' to the Jewish Temple) to convert to Judaism.
The time of exile, subsequent to the destruction of the physical Temple (due to our sins), is a time when "we no longer see our signs [of revealed Divinity]." In the Song of Songs it is described as a time when "I am asleep, yet my heart is awake." In sleep the eyes close, and so in exile the inner eye of the heart closes on the conscious plane of the soul ("I am asleep"), but it nonetheless remains open and awake on the unconscious plane ("yet my heart is awake"). The unconscious experience of the heart's inner eye is what inspires and motivates us, while still in exile, to devote our lives to Torah and good deeds.
In Kabbalah, Shabbat is wisdom (corresponding to the yud of God's essential Name Havayah), and "wisdom is the [primary experience of the] mind." The Temple is understanding (corresponding to the first hei of Havayah), and "understanding is [i.e., permeates] the [experience of the] heart." Wisdom is above time, and so Shabbat remains with us for eternity (for the essence of the mind and the experience of its inner eye is changeless). Now the visible Temple-site (understanding is associated with "place") is desolate (severe judgments manifest from understanding, not from wisdom; and the experience of the heart and its inner eye fluctuates, sometimes revealed and sometimes concealed), but it will soon be rebuilt with the coming of Mashiach. Then we will witness Godliness with the inner eye of our heart at a higher, more essential level than can be witnessed by the inner eye of the mind.