We show that a magnetic flux tube can grow in strength and size provided th
e temperature increases outward at the edge of the tube when the axial magn
etic field declines to its external value. The radius of the tube increases
at a rate determined by our theory. It is the coincidence of temperature a
nd magnetic field gradients of opposite sign that generates the new field,
and if this is lost the tube ceases to grow. The phenomenon is illustrated
by adopting plausible distributions for the temperature and magnetic field
strength, which yield an expression for the rate of growth of the magnetic
field magnitude B. The mechanism provides a possible explanation of the fib
rous nature of solar magnetic fields.