Capacitance needed to heat Nichrome wire 34°

Hi PF!

I'm working on a portable heating circuit. I'd like to use an ultracapacitor charged by 2 AA batteries to increase the temperature of 2.25m of 1mm Nichrome wire by 34° in 6 seconds.

The question is, what capacitance does the ultracapacitor have to have?

Initial values:
• Specific Heat of Nichrome: 450 J/(kg ∆K)
• Density of Nichrome: 8400 kg/m3
• Resistivity of Nichrome: 1e-6 Ωm

Calculated values:
• Mass of Nichrome: 0.015 kg = density*wire length*π*(wire diameter/2)^2
• Resistance of wire: 2.25e-6 Ω = resistivity/wire length
• Heat needed to cause temp change: 229.5 J = specific heat*mass*temp change
• Current needed for Joule heating: 10100 A = √(Heat needed/resistance of wire)
• Capacitance needed 51 F = heat needed / (0.5 * voltage^2)

So I'm confused about the relationship between the current needed to cause the appropriate Joule heating in the wire and the energy stored in the capacitor. Can anyone shed some light on this?

Thanks!

Michael