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.
Let's unpack this a bit. First, how does Jesus communicate with the Father if he and the Father are one and the same and not multiple persons? Dulle says in "Jesus' Prayers: It Doesn't Take Two Persons to Tango":
The reality of the incarnation and subsequent existential distinction
is so deep and profound that Jesus must relate to God as any other
human being would. There exists a phenomenological distinction between
Father and Son-from the Son's genuinely human point of view-due to His
acquisition of a human mind/consciousness in the incarnation.
Subsequent to the incarnation the Son relates to the Father as Other
even though, in fact, the Son and the Father are ultimately the same
divine person (but existing in two distinct modes of existence). Due
to Christ's genuine human point of view He can pray to the Father as
if the Father was a separate person, and love the Father as if loving
a separate person (as any human being would) even though the Son is
the same person as the Father. ... Communication requires the presence
of at least two minds, not necessarily two persons.
Second, how can this one person mediate between himself and humanity? Doesn't the need of a mediator indicate "you can't peaceably interact with them yourself"?
Trinitarians and modalists would agree that God needed to become a man in order to be our mediator. Trinitarians would say that the Son of God became the man Jesus and is our mediator by being both fully God and fully man and by interceding with the Father, who is a separate person from Jesus. Modalists would not say that. Dulle says in "A Oneness View of Jesus' Prayers":
The incarnation is God's one person coming to exist in a new way. God
did not change, but His manner of existence did. When God became a man
in the incarnation He began to exist as man in addition to His
existence as exclusive Spirit. God did not come to exist as another
"he," however. There was no creation of another person. Rather YHWH,
the only divine "he," came to exist in another manner than He had
existed for all eternity. Because God is the only personal subject in
Christ, the "he" in Christ is the same "he" as the "he" of the Father,
but existing in a new manner. The Father and Son, then, is the same
"he," but "he" is existing in two distinct ways. As Father "he" exists
as God, while as Son the same "he" has come to exist as man.
I also emailed Stan Hallett of Apostolic-Voice.org, and he said (among other things):
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
Summary: being a separate person is unnecessary for mediation. The game-changer of the incarnation accomplished enough on its own. He differs from Dulle in some regards*, but they would agree on that much.
* Dulle takes pains in two different articles to explain how Jesus and the Father communicate. Hallett seems in his email to deny they have any need to communicate, using Matthew 28 to say that Jesus acts on the Father's behalf.