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We studied the effects of thickness and heat treatments on giant magnetoimpedance (GMI) of cobalt-coated silver wires from 1 kHz to 100 MHz, under axial static magnetic field of 2 kOe. Cobalt, of thickness ranging from 1 to 25 μm, was electro-deposited on 47.7-μm-diameter silver wires. The frequency dependence of GMI varied with cobalt thickness with a maximum of 176% in 10-μm-thick cobalt at the characteristic frequency 2 MHz. The characteristic frequency decreased with increasing thickness of cobalt layer but it was rather insensitive to dc Joule heating and conventional furnace annealing. However, both heat treatments led to magnetic hardening and decrease in GMI ratio. Joule heating also induced anisotropy in wire structures normally dominated by axial anisotropy.