  We study a minimal extension to the Standard Model with an additional real
scalar triplet, $\Sigma$, and a single vector-like quark, $T$. This class of
models appear naturally in extensions of the Littlest Higgs model that
incorporate dark matter without the need of $T$-parity. We assume the limit
that the triplet does not develop a vacuum expectation value and that all
dimension five operators coupling the triplet to Standard Model fields and the
vector-like quarks are characterized by the scale $\Lambda$ at which we expect
new physics to arise. We introduce new non-renormalizable interactions between
the new scalar sector and fermion sector that allow mixing between the Standard
Model third generation up-type quark and the vector-like quark in a way that
leads to the cancellation of the leading quadratic divergences to the one-loop
corrections from the top quark to the mass of the Higgs boson. Within this
framework, new decay modes of the vector-like quark to the real scalar triplet
and SM particles arise and bring forth an opportunity to probe this model with
existing and future LHC data. We contrast constraints from direct colliders
searches with low energy precision measurements and find that heavy vector-like
top quarks with a mass as low as $650$ GeV are consistent with current
experimental constraints in models where new physics arises at scales below $2$
TeV.
