  Measurements of an object's temperature are important in many disciplines,
from astronomy to engineering, as are estimates of an object's spatial
configuration. We present the quantum optimal estimator for the temperature of
a distant body based on the black body radiation received in the far-field. We
also show how to perform separable quantum optimal estimates of the spatial
configuration of a distant object, i.e. imaging. In doing so we necessarily
deal with multi-parameter quantum estimation of incompatible observables, a
problem that is poorly understood. We compare our optimal observables to the
two mode analogue of lensed imaging and find that the latter is far from
optimal, even when compared to measurements which are separable. To prove the
optimality of the estimators we show that they minimise the cost function
weighted by the quantum Fisher information---this is equivalent to maximising
the average fidelity between the actual state and the estimated one.
