A solution to the problem of constant surface heating of an initially constant-temperature,
T
0
∗
T_0^*
, half-space where the material in question has a temperature-dependent thermal conductivity is obtained. The thermal conductivity,
k
∗
{k^*}
, is specifically given by
k
∗
=
k
0
∗
exp
[
λ
(
T
∗
−
T
0
∗
)
/
T
0
∗
]
{k^*} = k_0^*\exp \left [ {\lambda \left ( {{T^*} - T_0^*} \right )/T_0^*} \right ]
. The solution is valid for both heating and cooling of the material where
λ
\lambda
and
k
0
∗
k_0^*
are arbitrary in magnitude, and
λ
\lambda
can be either positive or negative in sign.