  Motivated by the recent interest on models with varying constants and whether
black hole physics can constrain such theories, two-dimensional charged stringy
black holes are considered. We exploit the role of two-dimensional stringy
black holes as toy models for exploring paradoxes which may lead to constrains
on a theory. A two-dimensional charged stringy black hole is investigated in
two different settings. Firstly, the two-dimensional black hole is treated as
an isolated object and secondly, it is contained in a thermal environment. In
both cases, it is shown that the temperature and the entropy of the
two-dimensional charged stringy black hole are decreased when its electric
charge is increased in time. By piecing together our results and previous ones,
we conclude that in the context of black hole thermodynamics one cannot derive
any model independent constraints for the varying constants. Therefore, it
seems that there aren't any varying constant theories that are out of favor
with black hole thermodynamics.
