Who are the modalists?

The ancient modalists were condemned heretics such as Noetus, Sabellius, and Praxeas. We don't have much record of their own writings, and what we do know of them is based on what men like Tertullian and Hippolytus wrote in response to them. So we know very little of their actual theology.

In modern times, Oneness Pentecostalism has revived modalism. Though some of them reject the term modalism, many do not, and it's just about universal that that's exactly what they teach.

Note that Unitarianism is the opposite heresy. Oneness believers say that the Father, Son, and Holy Spirit are all the same person, while Unitarians say that only the Father is fully God.

Jesus' role as mediator to Oneness believers

In researching this question, I emailed Jason Dulle of OnenessPentecostal.com. Here's what he said:

Yes, Jesus is our mediator. I think different Oneness adherents have different understandings of this. Some would say his mediatoral role is limited to the crucifixion. Others, such as myself, would say that role, while based on the atonement, is ongoing and will continue until the consummation of all things. This is no more problematic for our position that the issue of Jesus' communication with the Father while on Earth. The response is the same to both. For more information on how I understand the Father-Son distinction, see Avoiding the Achilles Heels of Trinitarianism, Modalistic Monarchianism, and Nestorianism: The Acknowledgement and Proper Placement of the Distinction Between Father and Son, A Oneness View of Jesus' Prayers, and Jesus' Prayers: It Doesn't Take Two Persons to Tango.

Dulle seems to summarize the differences between various Oneness views pretty well. His own views are rather unusual within that schema (positing two minds within the Godhead), but you can see a fuller discussion of them by accessing the revision history for this post.

Other Oneness theologians I contacted are consistent with each other in how they understand Jesus' role as mediator, though as Dulle said, they demonstrate disagreement over how "intercession" is to be understood.

For example, on the Oneness Q&A site Glorious Church, they affirm that "his mediatorial role is limited to the crucifixion:

1 Timothy 2:5-6 says, 'For there is one God and one Mediator between God and men, the Man Christ Jesus, who gave Himself a ransom for all....' From a Oneness perspective, we point out that the Mediator is specifically identified as 'the Man.' This agrees with Colossians 1:21-22, which says, 'And you, who once were alienated and enemies in your mind by wicked works, yet now He has reconciled in the body of His flesh through death.' Clearly the mediation and reconciliation between God and men was accomplished by means of the death of the Man, Jesus Christ, on the cross. We see the crucifixion as the once and for all intercession. We do not believe the Man Jesus is continuing to intercede in a literal way. We also believe that the Man who was crucified was God the Father in the flesh. We can make a distinction between God and His humanity, but we never want to think of them as two separate beings.

But in other ways, they agree with Dulle and the other theologians I contacted, all of whom believe that Jesus still intercedes for the church.

I also emailed William B. Chalfant, who has published Ancient Champions of Oneness as well as a number of historical novels about Sabellius. Chalfant engaged in a lengthy discussion of the key verses. Here are the highlights:

Of course, in my view, the term "Mediator" usually refers to someone fulfilling a designated role or position rather than necessarily dictating a discrete, substantive individual.

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We can admit that a "mediator" is a "mediator" between two parties, but, as Paul wrote, we must still conclude that "God is One" (Gal. 3:20).

It must be, then, that God has "mediated" through His incarnation as the Messiah."God was in Christ": that is the incarnation.

The "mediator" is the "man Christ Jesus" and not a second divine person as some would have it.

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Notice in this passage [1 John 2:1-2] that Jesus is identified as the "Paraclete" by John, who also wrote the Gospel of John, where Jesus promises, after his earthly demise and resurrection, the coming of the "Paraclete". Oneness teachers identify Jesus as the "Paraclete" (that is, the Spirit of Christ is the Holy Spirit". Paul affirms that in teaching that there is "one Spirit" (Ephesians 4:4). And so we would see if there is any post-resurrection "mediation" is will be done by the Spirit of Christ (the Holy Spirit).

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Again, "mediation" seems to refer to the earthly ministry of the Incarnation (God the Father manifested in the flesh), while "intercession" is again accomplished by the risen Christ (who is God the Father manifested in the glorified flesh).

In short, the terms "mediator", "intercessor", "reconciliation", when expressed in relation to the exigencies of the "incarnation" (enfleshment of God the Father), who now subsists as the Eternal Spirit in the glorified Man Christ Jesus, in a substantive henosis or union.

I also emailed Stan Hallett of Apostolic-Voice.org. His words serve as a decent summary of Chalfant's:

In my view He is intercessor or mediator because He is the door (John 10:9). No man comes to the Father but by Him (John 14:6).

I do not believe that He needs to go a talk to the Father on our behalf as some other person of a Trinitarian Godhead, for all power was given to him in heaven and in earth (Matthew 28:18).

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God needed to come to redeem man unto himself (Titus 2:13,14). The annual shedding the blood of bulls and sheep could not redeem us (Hebrews 10:4). Therefore the scripture says that God redeemed us with His own blood.

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God did not send someone else to pay the price for sin, He came Himself.

The common view of each of these theologians can be summarized as:

Being a separate person is unnecessary for mediation. The game-changer of the incarnation accomplished enough on its own. I believe each of them would affirm this statement whole-heartedly, with the possible exception of Dulle, who would give it a bit more nuance.