  Polar precipitation archived in ice caps contains information on past
temperature conditions. Such information can be retrieved by measuring the
water isotopic signals of $\delta{}^{18}\mathrm{O}$ and $\delta\mathrm{D}$ in
ice cores. These signals have been attenuated during densification due to
molecular diffusion in the firn column, where the magnitude of the diffusion is
isotopologoue specific and temperature dependent. By utilizing the differential
diffusion signal, dual isotope measurements of $\delta{}^{18}\mathrm{O}$ and
$\delta\mathrm{D}$ enable multiple temperature reconstruction techniques. This
study assesses how well six different methods can be used to reconstruct past
surface temperatures from the diffusion-based temperature proxies. Two of the
methods are based on the single diffusion lengths of $\delta{}^{18}\mathrm{O}$
and $\delta\mathrm{D}$, three of the methods employ the differential diffusion
signal, while the last uses the ratio between the single diffusion lengths. All
techniques are tested on synthetic data in order to evaluate their accuracy and
precision. We perform a benchmark test to thirteen high resolution Holocene
data sets from Greenland and Antarctica, which represent a broad range of mean
annual surface temperatures and accumulation rates. Based on the benchmark
test, we comment on the accuracy and precision of the methods. Both the
benchmark test and the synthetic data test demonstrate that the most precise
reconstructions are obtained when using the single isotope diffusion lengths,
with precisions of approximately $1.0\,^\mathrm{o}\mathrm{C}$. In the benchmark
test, the single isotope diffusion lengths are also found to reconstruct
consistent temperatures with a root-mean-square-deviation of
$0.7\,^\mathrm{o}\mathrm{C}$.
