  We show that nonlinear transport responses in strange metals are strong,
larger by a factor of $E_F/T$ than in Fermi liquids. Within the two-dimensional
Yukawa-Sachdev-Ye-Kitaev model of a Fermi surface with a spatially random
coupling to a critical scalar, the third order conductivity is found to diverge
as $1/T$ at low $T$, indicating the existence of a voltage-temperature scaling
regime in the conductance. Its frequency and orientation dependence contains
information on relaxation times of heat and electron distribution deformations,
providing a new set of tools to characterize strange metals.
