  We propose a method to map the temperature distribution of the hot gas in
galaxy clusters that uses resolved images of the thermal Sunyaev-Zel'dovich
(tSZ) effect in combination with X-ray data. Application to images from the New
IRAM KIDs Array (NIKA) and XMM-Newton allows us to measure and determine the
spatial distribution of the gas temperature in the merging cluster MACS
J0717.5+3745, at $z=0.55$. Despite the complexity of the target object, we find
a good morphological agreement between the temperature maps derived from X-ray
spectroscopy only -- using XMM-Newton ($T_{\rm XMM}$) and Chandra ($T_{\rm
CXO}$) -- and the new gas-mass-weighted tSZ+X-ray imaging method ($T_{\rm
SZ}$). We correlate the temperatures from tSZ+X-ray imaging and those from
X-ray spectroscopy alone and find that $T_{\rm SZ}$ is higher than $T_{\rm
XMM}$ and lower than $T_{\rm CXO}$ by $\sim 10\%$ in both cases. Our results
are limited by uncertainties in the geometry of the cluster gas, contamination
from kinetic SZ ($\sim 10\%$), and the absolute calibration of the tSZ map
($7\%$). Investigation using a larger sample of clusters would help minimise
these effects.
