  We test asteroseismic radii of Kepler main-sequence and subgiant stars by
deriving their parallaxes which are compared with those of the first Gaia data
release. We compute radii based on the asteroseismic scaling relations as well
as by fitting observed oscillation frequencies to stellar models for a subset
of the sample, and test the impact of using effective temperatures from either
spectroscopy or the infrared flux method. An offset of 3%, showing no
dependency on any stellar parameters, is found between seismic parallaxes
derived from frequency modelling and those from Gaia. For parallaxes based on
radii from the scaling relations, a smaller offset is found on average;
however, the offset becomes temperature dependent which we interpret as
problems with the scaling relations at high stellar temperatures. Using the
hotter infrared flux method temperature scale, there is no indication that
radii from the scaling relations are inaccurate by more than about 5%. Taking
the radii and masses from the modelling of individual frequencies as reference
values, we seek to correct the scaling relations for the observed temperature
trend. This analysis indicates that the scaling relations systematically
overestimate radii and masses at high temperatures, and that they are accurate
to within 5% in radius and 13% in mass for main-sequence stars with
temperatures below 6400 K. However, further analysis is required to test the
validity of the corrections on a star-by-star basis and for more evolved stars.
