At the time of going to print yesterday, with almost 300 of a possible 871 votes yet to be recorded, Ms Heath was polling second highest in the Murrumbidgee ward.
With just over 29 per cent of the vote so far, she has amassed 163 first preference votes.
She is likely to take the place of Patrick Brown on council.
Mr Brown so far has only 69 votes (or 12 per cent).
The ward’s other candidates, Robert Curphey and Judith Saxvik, are likely to retain their seats on council at the close of the polls.
Mr Curphey has the strongest support from voters so far, with his 194 votes representing 35 per cent of first preferences reported.
Ms Saxvik so far has 128 votes (23 per cent).
Murrumbidgee was the only Murrumbidgee Council ward to go to a vote on Saturday, with only the minimum number of candidates registered for Murrumbidgee East and Jerilderie.
In both of those wards, sitting councillors were the only candidates.
Retaining a seat on council in the Jerilderie ward is current Mayor Ruth McRae, Faith Bryce and Troy Mauger.
Automatically re-elected in the Murrumbidgee East ward are Robert Black, Christine Chirgwin and Timothy Strachan.
There was no vote in the Berrigan Shire on Saturday, as it only had seven candidates register for eight council seats.
All seven candidates - returning councillors Julia Cornwell McKean, Matthew Hannan and Renee Pain, and newcomers Catherine Healy, Renee Brooker, John Stringer and Kate Ngatokoa - will be automatically elected.
A by-election will be held on November 23 to fill the vacancy. Nominations will open on October 14, and will close on October 23.
To date only first preference votes have been counted for Murrumbidgee, after which the NSW Electoral Commission will continue with preferences until they have three candidates meet quota.
The final quota will be set once all first preference votes have been recorded.
With postal votes not closing until September 27, this distribution of preferences is not expected to start until September 30.
The NSW Electoral Commission anticipates the election to be officially declared on October 3.