  We explore preheating in multi-field models of inflation in which the
field-space metric is a highly curved hyperbolic manifold. One broad family of
such models is called $\alpha$-attractors, whose single-field regimes have been
extensively studied in the context of inflation and supergravity. We focus on a
simple two-field generalization of the $T$-model, which has received renewed
attention in the literature. Krajewski et al. concluded, using lattice
simulations, that multi-field effects can dramatically speed-up preheating. We
recover their results and further demonstrate that significant analytical
progress can be made for preheating in these models using the WKB approximation
and Floquet analysis. We find a simple scaling behavior of the Floquet
exponents for large values of the field-space curvature, that enables a quick
estimation of the $T$-model reheating efficiency for any large value of the
field-space curvature. In this regime we further observe and explain universal
preheating features that arise for different values of the potential steepness.
In general preheating is faster for larger negative values of the field-space
curvature and steeper potentials. For very highly curved field-space manifolds
preheating is essentially instantaneous.
