  Classical Cepheids are the most popular distance indicators and tracers of
young stellar populations. The key advantage is that they are bright and they
can be easily identified in Local Group and Local Volume galaxies. Their
evolutionary and pulsation properties depend on their chemical abundances. The
main aim of this investigation is to perform a new and accurate abundance
analysis of two tens of calibrating Galactic Cepheids using high spectral
resolution (R$\sim$40,000-115,000) and high S/N spectra ($\sim$400) covering
the entire pulsation cycle. We focus our attention on possible systematics
affecting the estimate of atmospheric parameters and elemental abundances along
the pulsation cycle. We cleaned the line list by using atomic transition
parameters based on laboratory measurements and by removing lines that are
either blended or display abundance variations along the pulsation cycle. The
spectroscopic approach that we developed brings forward small dispersions in
the variation of the atmospheric parameters ($\sigma$($T_{\rm eff}$)$\sim$50 K,
$\sigma$($\log{g}$)$\sim$0.2 dex, and $\sigma$($\xi$)$\sim$0.2 km/s) and in the
abundance of both iron ($\lesssim$ 0.05 dex) and alpha elements ($\lesssim$0.10
dex) over the entire pulsation cycle. We also provide new and accurate
effective temperature templates by splitting the calibrating Cepheids into four
different period bins, ranging from short to long periods. For each period bin,
we performed an analytical fit with Fourier series providing $\theta =
5040/{T_{\rm eff}}$ as a function of the pulsation phase. The current findings
are a good viaticum to trace the chemical enrichment of the Galactic thin disk
by using classical Cepheids and a fundamental stepping stone for further
investigations into the more metal-poor regime typical of Magellanic Cepheids.
