How do I heat a wire around a pot to heat up the soil within
as others mentioned: you need a large battery or better yet a mains powered source for this to run for an extended amount of time.

don't use a resistor in series with the wire. Otherwise you will heat the resistor, but not the wire. The wire itself should be the (only) resistor.

the wire resistor has to have a resistance of R=V^2/P. V is the available voltage and P the desired power. This can be pretty high if the voltage is high and desired power is low. In that case a very long and thin wire is needed if you use copper which is highly conductive. For heater wire, typically you use a material with worse conduction.

If you want to heat large portions of soil homogeneously, run the (insulated) wires through the soil and not around the pot. The soil has good thermal isolation, so peripheral heating would not heat the interior by much.