The good news is that epoxy is pretty forgiving with regards to cure temperatures. While cooler temperatures slow down the process, inevitably it will always cure - whether it be with enough time, or when the temperature warms up. Other resins, such as polyester, can have the entire cure process disrupted by cooler temperatures, and never harden.
Having said that, cooler temperatures do pose probems - in particular with application. Unlike liquids such as water the viscosity of epoxy changes with temperature. The warmer it gets, the less viscous it becomes. In cooler temperatures the epoxy becomes like honey and is hard to apply. Overall, for ideal results, it's best to bring your shop to room temperature or higher. If you're able to seal your tarp tent reasonably, you should be able to heat it with some type of blast furnace. Just be sure to take precautions for carbon monoxide buildup.
Once you've applied the epoxy, it's less important to maintain a high temperature, and you can drop it a bit. It's actually good to drop the temperature a bit if you've just applied a fresh coat over wood, as it will prevent outgassing (outgassing causes bubbles in the epoxy as gas is emited from wood in rising temperatures). Probably good to keep it above 10 degrees centigrade (50F) while curing (it will take a long time to cure at this temp). It does vary from manufacturer to manufacturer, so always best to consult the instructions.