  Collapse models constitute an alternative to quantum mechanics that solve the
well-know quantum measurement problem. In this framework, a novel approach to
include dissipation in collapse models has been recently proposed, and awaits
experimental validation. Our work establishes experimental bounds on the
so-constructed linear-friction dissipative Di\'osi-Penrose (dDP) and Continuous
Spontaneous localisation (dCSL) models by exploiting experiments in the field
of levitated optomechanics. Our results in the dDP case exclude collapse
temperatures below $ 10^{-13}$K and $ 6 \times 10^{-12}$K respectively for
values of the localisation length smaller than $10^{-6}$m and $10^{-8}$m. In
the dCSL case the entire parameter space is excluded for values of the
temperature lower than $6 \times 10^{-9}$K.
