Is there a formula to determine heat output of a wire with current applied?
If you're heating plants then you don't care about wire temperature much - just the power requirements. You can calculate this from \$ P = VI = I^2R = \frac {V^2} R \$, the variations coming from substitutions from Ohm's law, \$ V = IR \$.
The temperature will stabilise at the point where heat lost = power in. The problem is that modelling heat loss can get quite complex.
The standard means of achieving what you want is to use an over-powered heater and a temperature sensor to either switch off or reduce power to maintain soil temperature. That way you can get repeatable temperature control even when the ambient conditions change.