"He doesn't say much about fighting actual opposition until near the end of the letter:

Rom 16:17-19
17 Now I beseech you, brethren, mark them which cause divisions and offences contrary to
   the doctrine which you have learned; and avoid them.

He has just dealt with the division that his opposition caused in Corinth. And he has nothing
good to say about such men:

18 For they that are such serve not our Lord Jesus Christ, but their own belly; and by good
   words and fair speeches deceive the hearts of the simple.

The heresy may not have come to Rome yet but I think Paul expects it to come. And we see
here that when it comes, Paul knows that it will not just be a wrong emphasis, or a trying
to be over-righteous, but actual evil:

19 For your obedience is come abroad unto all men. I am glad therefore on your behalf: but yet
   I would have you wise unto that which is good, and simple concerning evil.

He is commending their obedience to the word of God. And warns them, I think, not to be
taken in by a heresy that claims to be wisdom but is actually evil.

That is about all that Paul says directly against heresy. It's not much."

However, I reserve the right to be wrong about my 7/2017 opinion on this issue.

The warning in chapter 16 may have not been addressed to the church at Rome, as the heresy might not have been taught there yet.

There are some indications that Romans 16 was addressed to Ephesus:

1) The letter to the Romans would end quite satisfactorily with Romans 15:
30 Now I beseech you, brethren, for the Lord Jesus Christ's sake, and for the love of the Spirit, that ye strive together with me in your prayers to God for me;
31 That I may be delivered from them that do not believe in Judaea; and that my service which I have for Jerusalem may be accepted of the saints;
32 That I may come unto you with joy by the will of God, and may with you be refreshed.
33 Now the God of peace be with you all. Amen.

2) He greets Priscilla and Aquila. They had moved to Corinth from Rome, and then moved to Ephesus. Paul is writing Romans probably a couple of years after their move to Ephesus and so they could conceivably have moved back to Rome. But the last we know of them from Paul's and Luke's writings is that they were in Ephesus.

3) He greets Epaenetus, who is the firstfruits of Achaia (or more probably, Asia)
This is "Asia" in many translations. Adam Clarke: " Asia, is the reading of ABCDEFG, some others; the Coptic, Ethiopic, Armenian, Vulgate, and Itala; and some of the chief of the fathers."

4) Since Paul had just written Galatians against the heresy that was spreading in the Anatolian peninsula it would not be unreasonable that Paul would address a warning such as Rom 16:17-18 to Ephesus.

5) The sheer number of people addressed in chapter 16 is, I think, remarkable of a church that he has never visited. (a 'least' 34 - counting only 2 for 'household', 'the brethren' and 'all the saints'.) Such a number is easily believable for Ephesus.

6) This is a small thing, but if chapter 16 was tacked on, then the commendation of "Phebe ... a servant of the church which is at Cenchrea" was only addressed to Ephesus. Corinth itself is on the Ionian Sea, facing Italy. Cenchrea is the port on the Aegean Sea, facing Ephesus. Why, if chapter 16 was going west, did Paul send it with a resident of the east-facing port?

7) And I have been wondering why Paul labored so long on this letter of Romans only to send it to one congregation -- one that he has never visited. I take Ephesians as a possible parallel case. It seems that at the same time that he wrote Colossians to the source of a problem, he wrote Ephesians as a general epistle to address the problem in a more general way and probably sent it to several congregations in Asia (indicated by the letter to Laodicea mentioned in Colossians). If he would write a general epistle of 6 chapters and send it to multiple congregations, why write such a masterpiece as Romans' 15 or 16 chapters and send it to only one congregation?
A broad clarification such as the letter to the Romans provides might have been viewed as a great help to Ephesus with the problem in Galatia in mind. Romans is written on the heels of Galatians, and it might have seemed very possible that the false teachers in Galatia would soon make their way west to Asia. Or those in Corinth might move east to Ephesus.
Just perhaps, he wrote Romans and sent it to Rome, but also had a copy of it made and sent to Ephesus. And if so, might have tacked on what we have in chapter 16 as greetings to so many that he knew there.
It may have been this extended copy of Romans that was preserved in the New Testament. Just as it looks like the copy of Ephesians that was sent to Ephesus was also the copy that was preserved in the canon. Both may have been drawn from the archives of the Ephesus church.

It turns out that I am not alone in suggesting the possibility that Romans 16 was tacked onto a copy of Romans that was sent to Ephesus:

The Early Christians in Ephesus by Paul Trebilco, 2004, p.88
There are various constructs of the end of Romans:
"Note that the oldest papyrus manuscript p(46) lacks Rom 15:1-23 and other manuscripts have Rom 16:25-7 after Rom 15:33 or 14:23, or after both 14:23 and in its present place. ...
The Ephesian destination of the letter is based on 1) the greetings sent to Priscilla and Aquila who were in Ephesus when Paul wrote 1 Cor.; 2) Epaenetus is described as the "first convert to Christ in Asia; 3) Rom 16:17-20 seems more suited to an Ephesian rather than a Roman provenance. ...
Manson (1962, p225-41) thought Paul sent Rom 1-15 to Rome and another copy of the letter which included chapter 16 to Ephesus. "
Discovering Romans, by Anthony C. Thiselton, p59 "T.W. Manson ... His theory is accepted by Munck, Leehardt and Bultmann"
(T. W. Manson (1893-1958) 1953 Moderator of the General Assembly, of the Presbyterian Church of England. Yates Professor of New Testament Greek and Exegesis at Mansfield College, Oxford, 1932-1936, Rylands Professor of Biblical Criticism and Exegesis in the University of Manchester. A Doctor of Divinity of the Universities of Cambridge, Dublin, Durham and Glasgow. Among his many publications: The Sayings of Jesus. One of the founder-Editors of the Studies in Biblical Theology and Ethics and The Gospel (SCM Press) and The Teaching of Jesus and The Servant Messiah.)