The transient behaviour of high-temperature superconductor (HTS) curre
nt leads operated between liquid helium and liquid nitrogen temperatur
es is analysed for burnout conditions upon transition of the HTS into
the normal state. Leads composed of HTS only and of HTS sheathed by pu
re silver or silver alloy are investigated numerically for temperature
-dependent properties and analytically for temperature-independent pro
perties. For lower values of shape factor (current density times lengt
h), the lead can be operated indefinitely without burnout. At higher v
alues of shape factor, the lead reaches burnout in a finite time. With
high current densities, the leads heat adiabatically. For a fixed sha
pe factor, low current densities are desired to achieve long burnout t
imes. To achieve a low helium boil-off rate in the superconducting sta
te without danger of burnout, there is a preferred temperature depende
nce for thermal conductivity, and silver alloy sheaths are preferred t
o pure silver sheaths. However, for a given current density, pure silv
er sheaths take longer to burn out.