  A recent sensitivity study has shown that the $^{35}$K$(p,\gamma)^{36}$Ca
reaction is one of the ten $(p,\gamma)$ reaction rates that could significantly
impact the shape of the calculated X-ray burst light curve. In this work, we
propose to reinvestigate the $^{35}$K$(p,\gamma)^{36}$Ca reaction rate, as well
as related uncertainties, by determining the energies and decay branching
ratios of $^{36}$Ca levels, within the Gamow window, in the 0.5 to 2 GK X-ray
burst temperature range. These properties were studied using the one neutron
pick-up transfer reaction $^{37}$Ca$(p,d)^{36}$Ca in inverse kinematics using a
radioactive beam of $^{37}$Ca at 48 MeV nucleon$^{-1}$. The experiment
performed at GANIL, used the liquid Hydrogen target CRYPTA, the MUST2 detector
array for the detection of the light charged particles and a zero degree
detection system for the outgoing heavy ions. The atomic mass of $^{36}$Ca is
confirmed and new resonances have been proposed together with their proton
decay branching ratios. This spectroscopic information, used in combination
with recent theoretical predictions for the $\gamma$-width, were used to
calculate the $^{35}$K$(p,\gamma)^{36}$Ca reaction rate. The recommended rate
of the present work was obtain within a uncertainty factor of 2 at 1 sigma.
This is consistent, with the previous estimate in the X-ray burst temperature
range. A large increase of the reaction rate was found at higher temperatures
due to two newly discovered resonances. The $^{35}$K$(p,\gamma)^{36}$Ca
thermonuclear reaction rate is now well constrained by the present work in a
broad range of temperatures. Our results show that the
$^{35}$K$(p,\gamma)^{36}$Ca reaction does not affect the shape of the X-ray
burst light curve, and that it can be removed from the list of the few
influential proton radiative captures reactions having a strong impact on the
light curve.
