  We construct new static, spherically symmetric non-extremal black hole
solutions of four-dimensional ${\cal N}=2$ supergravity, using a systematic
technique based on dimensional reduction over time (the c-map) and the real
formulation of special geometry. For a certain class of models we actually
obtain the general solution to the full second order equations of motion,
whilst for other classes of models, such as those obtainable by dimensional
reduction from five dimensions, heterotic tree-level models, and type-II
Calabi-Yau compactifications in the large volume limit a partial set of
solutions are found. When considering specifically non-extremal black hole
solutions we find that regularity conditions reduce the number of integration
constants by one half. Such solutions satisfy a unique set of first order
equations, which we identify.
  Several models are investigated in detail, including examples of
non-homogeneous spaces such as the quantum deformed $STU$ model. Though we
focus on static, spherically symmetric solutions of ungauged supergravity, the
method is adaptable to other types of solutions and to gauged supergravity.
