Yes, the passage clearly, unambiguously says that this is the same Spirit, because by the phrase "But ye are not in the flesh, but in the Spirit", Paul separates his addressees from those who are fleshly, possess no Spirit, and thus are able neither to contemplate about spiritual realities, nor to please God (cf. Romans 8:5-8), stating immediately the condition for this separation "if Spirit of God dwells in you". Then he again returns to the very same people who possess not the Spirit by the phrase "now, if any man have not the Spirit of Christ, he is none of his", that is to say, those "none of his" refer to those Spirit-deprived, from whom Paul has just in previous sentences separated the Spirit-possessors (for there is no other class of humans but Spirit-possessors and the Spirit-deprived); now, if the principle of this separation is the Spirit in the phrase "Spirit of God", then how can the "Spirit of Christ" Which (or rather Who) is the principle of the very same separation possibly be any other Spirit but the very same Spirit?
Again, Paul is emphatic that the Spirit of God is the Spirit of Christ also in 1 Cor. 2:14-16, saying that those who possess not Spirit cannot understand things that come from the Spirit of God, and then in verse 14 he quotes Isaiah 40:13 and semantically with the absolutely identical meaning calls the just-quoted "Spirit of God" - the "Mind of Lord", and immediately claims that also we, Christians possess the very same Mind, called now "the Mind of Christ", and thus, the "Spirit of Christ", since the "Mind" and "Spirit" are used interchangeably in 1 Cor. 2:14-16; and, moreover, since "Mind of Lord" of Isaiah is identified with "Mind of Christ", and since the "Lord" in Isaiah is identified with God, then Christ is also identified with God. That is why, Christ does not "possess" (ἔχει) Spirit, and Spirit does not "dwell" (οἰκέι) in Him (in the manner the Spirit is possessed by and dwells in us), but the Spirit is called "Christ's Spirit" just with the same power and semantics as in the expression of "God's Spirit" or "Father's Spirit" or "Lord's Spirit". But neither is Christ identical with Father, being the Latter's Son, yet to both of Them the Spirit belongs in the intrinsic and essential manner and not in the manner of participation or bestowal like in us.
Logos is the very Truth (John 14:6), and the Holy Spirit is the "Spirit of Truth" (John 16:13).
And yes, as you have mentioned, the human heart is the eternal throne and dwelling place of the Father and the Son (John 14:23); but also of the Spirit, for only through Spirit we can understand and acclaim the divinity of Christ (1 Cor. 12:3), and only through Spirit the new Israel will be able to worship the Father (John 4:24), for the condition of true and rightful worshiping of the Father is the just-mentioned acclamation of the divinity of the Son (Phil. 2:11); and just as God's Son, so also God's Spirit will dwell eternally in heart of man, who is, therefore, the Spirit's living temple (1 Cor. 6:19).
Thus, human heart is the Throne of Holy Trinity.