The plea followed his admission that he had burned coal to try to keep warm in the old house.
"Come the first of January, we'll be the first to receive an infringement notice," he said.
His situation highlighted that while the town had four or five years' notice of stricter burning regulations banning open fires - which come into force in January - there were still houses that were "extraordinarily difficult to heat", he said.
"I may as well have slept under a tree. We do not want to see people freeze to death, either, especially myself," the former Roxburgh farmer said.
Cr Eckhoff's comments were made on Wednesday as the natural resources committee discussed winter air quality results and progress that needed to be made in the next few years.
Chief executive Graeme Martin said the council would need to change its educative approach because there would be significant public pressure about the use of coal.
Part of that would be an education programme targeting owners of rental accommodation. In other centres those people were the last to insulate or provide compliant heating, he said.
Natural resources and environmental information director John Threlfall said changing human nature was difficult.
A strategy covering the next 12 months was being developed to cover issues like enforcement.
For less polluted areas, such as Dunedin and Balclutha, the changeover to compliant burners or electricity through natural attrition was taking longer than had been hoped, but come the council's deadline of 2013 - or the government's 2016 and 2020 deadlines - he was confident the downward trend in emissions would be "there or thereabouts".
It would not happen on its own so there was significant work to be done educating people, he said.
Recent publicity about not being able to use coal had resulted in 90 applications for assistance in six weeks.
Chairman Stephen Woodhead said the air quality report gave the council some hope it could meet its targets and that communities like Alexandra were making progress, even if they had a long way to go.
Yesterday, at a policy and submissions committee meeting, councillors endorsed the proposal to change its air plan to include Milton in the same category as Central Otago towns, and to move Lawrence into the same category as Dunedin and Balclutha.
Milton had similar air pollution to Arrowtown and only 20% of its homes had compliant burners.
The change would include a transition period, possibly of up to five years, for the two towns to comply.
