  Well-tempering is a promising classical method of dynamically screening an
arbitrarily large vacuum energy and generating a late-time, low energy de
Sitter vacuum state. In this paper, we study for the first time self-tuning in
teleparallel gravity and obtain well-tempered cosmological models in the
teleparallel gravity analogue of Horndeski theory. This broadens the scope of
well-tempered cosmology and teases the potentially far richer cosmological
dynamics that could be anchored on teleperallel gravity. We expand the
well-tempered recipe to its most general form so far and use it to search for
the first well-tempered cosmologies in teleparallel gravity. We also study the
cosmological dynamics in a well-tempered model and demonstrate the dynamical
stability of the vacuum, the compatibility with a matter era, and the stability
of the vacuum through a phase transition.
