At what temperature does concrete stop curing?

I am in the northeast and just poured some footings and 8" concrete sonotubes yesterday. The temperature was 50F. Today the temperature was low 40's and tonight low 20's. I covered the tubes with lots of hay and poly tarps over top. I did not use any curing accelerators or antifreeze.
My concern is the temperature will be going steadily down and in a week or 2 the high temp might be only around 32. No matter how much hay and tarps I put over the concrete, eventually the ground around it will freeze. I understand that concrete should not be allowed to freeze until it has reached a certain strength.
I also read that concrete effectively stops curing below 40F, but I am not sure about that. I can keep the concrete from freezing for about 3 weeks more, but I may not be able to get it above to 40F during that time. Will the concrete still cure to the desired strength so that it will not be damaged by eventual winter freeze? Thanks,
-- Jeff
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No worrys! Concrete gains approx. 70% of its strength in the first week and if you poured high/early mix-it's quicker. Concrete is an exothermic reaction (genrates its own heat), so trapping that heat with hay and tarps combined with the latent heat radiating from the ground will provide adequate protection for a good cure.
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