How do modalists understand the role of Jesus as mediator? The Bible calls Jesus our mediator:

Christ Jesus is the one who died—more than that, who was raised—who is at the right hand of God, who indeed is interceding for us. (Romans 8:34, ESV)
For there is one God, and there is one mediator between God and men, the man Christ Jesus, (1 Timothy 2:5, ESV)
Consequently, he [Jesus] is able to save to the uttermost those who draw near to God through him, since he always lives to make intercession for them. (Hebrews 7:25, ESV)

Trinitarians believe that Jesus intercedes with the Father on our behalf. He can do this because he is a distinct person, and he is the only competent mediator because only God can truly mediate with himself.
Modalism teaches that the Father, Son and Holy Spirit are &quot;different modes or aspects of the One God, as perceived by the believer, rather than three coeternal persons within the Godhead.&quot; (Wikipedia)
If God is not multiple people, how can Jesus intercede with the father? How do modalists understand the role of Jesus as mediator?
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.


Dulles 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 Dulles said, they demonstrate disagreement over how "intercession" is to be understood.

For example, on the Oneness Q&amp;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 Dulles 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.
  
  ...
  
  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.
  
  ...
  
  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).
  
  ...
  
  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).
  
  ...
  
  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.
  
  ...
  
  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 Dulles, who would give it a bit more nuance.