  The three-omega method, a powerful technique to measure the thermal
conductivity of nanometer-thick films and the interfaces between them, has
historically employed straight conductive wires to act as both heaters and
thermometers. When investigating stochastically prepared samples such as
two-dimensional materials and nanomembranes, residue and excess material can
make it difficult to fit the required millimeter-long straight wire on the
sample surface. There are currently no available criteria for how diverting
three-omega heater wires around obstacles affects the validity of the thermal
measurement. In this Letter, we quantify the effect of wire curvature by
performing three-omega experiments with a wide range of frequencies using both
curved and straight heater geometries on SiO$_2$/Si samples. When the heating
wire is curved, we find that the measured Si substrate thermal conductivity
changes by only 0.2%. Similarly, we find that wire curvature has no significant
effect on the determination of the thermal resistance of a $\sim$65 nm SiO$_2$
layer, even for the sharpest corners considered here, for which the largest
measured ratio of the thermal penetration depth of the applied thermal wave to
radius of curvature of the heating wire is 4.3. This result provides useful
design criteria for three-omega experiments by setting a lower bound for the
maximum ratio of thermal penetration depth to wire radius of curvature.
