All epoxy paints consist of a resin and an hardener. They are mixed together in proper ratios so that there is just enough hardener to react with the resin. In theory, none of either part is left over, hence no long-term off-gassing. There will be a curing time for the paint/adhesive to reach maximum strength. Different epoxies have different cure times. I doubt it will be longer than a week or two, but the applicator will be able to advise on cure time. It should be solid to the touch in 24 hours at the most.
You can begin to look for applicators on the internet. Just search for Epoxy Applicator South Dakota. A 3M distributor comes up with an office in South Dakota. Or go to manufacturers’ home pages such as Rustoleum, Sherman Williams, or Krylon and search for distributors in your area. Check references for coatings and applicators in your area.
The temperature of the inside floor to be coated is important. The only way the outside temperature will have any affect is if it makes the inside floor cold. Most epoxies do need to have a specific temperature to cure properly. If the floor is too cold, it may take a long time to cure or not cure at all and may not be as strong as necessary. For all these reasons, hire an experienced applicator who knows what they are doing and use a good quality paint that they recommend. I do not advise applying an epoxy paint yourself if you do not have previous experience. Protective equipment may be required during application, possibly even a self-contained breathing apparatus.
If the carpet is in good condition, why not leave it?