  We announce the discovery of two planets orbiting the M dwarfs GJ 251
($0.360\pm0.015$ M$_\odot$) and HD 238090 ($0.578\pm0.021$ M$_\odot$) based on
CARMENES radial velocity (RV) data. In addition, we independently confirm with
CARMENES data the existence of Lalande 21185 b, a planet that has recently been
discovered with the SOPHIE spectrograph. All three planets belong to the class
of warm or temperate super-Earths and share similar properties. The orbital
periods are 14.24 d, 13.67 d, and 12.95 d and the minimum masses are
$4.0\pm0.4$ $M_\oplus$, $6.9\pm0.9$ $M_\oplus$, and $2.7\pm0.3$ $M_\oplus$ for
GJ 251 b, HD 238090 b, and Lalande 21185 b, respectively. Based on the orbital
and stellar properties, we estimate equilibrium temperatures of $351.0\pm1.4$ K
for GJ 251 b, $469.6\pm2.6$ K for HD 238090 b, and $370.1\pm6.8$ K for Lalande
21185 b. For the latter we resolve the daily aliases that were present in the
SOPHIE data and that hindered an unambiguous determination of the orbital
period. We find no significant signals in any of our spectral activity
indicators at the planetary periods. The RV observations were accompanied by
contemporaneous photometric observations. We derive stellar rotation periods of
$122.1\pm2.2$ d and $96.7\pm3.7$ d for GJ 251 and HD 238090, respectively. The
RV data of all three stars exhibit significant signals at the rotational period
or its first harmonic. For GJ 251 and Lalande 21185, we also find long-period
signals around 600 d, and 2900 d, respectively, which we tentatively attribute
to long-term magnetic cycles. We apply a Bayesian approach to carefully model
the Keplerian signals simultaneously with the stellar activity using Gaussian
process regression models and extensively search for additional significant
planetary signals hidden behind the stellar activity.
