  We study the contributions of colorless vectorlike fermions to the triple
gauge couplings $W^+ W^- \gamma$ and $W^+ W^- Z^0$. We consider models in which
their coupling to the Standard Model Higgs boson is allowed or forbidden by
quantum numbers. We assess the sensitivity of the future accelerators FCC-ee,
ILC and CLIC to the parameters of these models, assuming they will be able to
constrain the anomalous triple gauge couplings with a precision $\delta
\kappa_V \sim \mathcal{O}(10^{-4})$, $V=\gamma,Z^0$. We show that the
combination of measurements at different center-of-mass energies helps to
improve the sensitivity to the contribution of vectorlike fermions, in
particular when they couple to the Higgs. In fact, the measurements at the
FCC-ee and, especially, the ILC and the CLIC, may turn the triple gauge
couplings into a new set of precision parameters able to constrain the models
better than the oblique parameters or the $H \to \gamma \gamma$ decay, even
assuming the considerable improvement of the latter measurements achievable at
the new machines.
