  Most deterministic schemes for controlling temperature by kinetic variables
(NH thermsotat), configurational variables (BT thermostat) and all phase space
variables (PB thermostat) are non-ergodic for systems with a few degrees of
freedom. While for the NH thermostat ergodicity has been achieved by
controlling the higher order moments of kinetic energy, the issues of
nonergodicity of BT and PB thermostats still persist. In this paper, we propose
a family of modifications for improving their ergodic characteristics. To do
so, we introduce two new measures of configurational temperature (second and
third order) based on the generalized temperature - curvature relationship. The
equations of motion for the existing thermostats are modified by controlling
the relevant higher order temperature variables. The ergodic characteristics of
the proposed modifications are tested using a single harmonic oscillator. For
the PB thermostat, the fastest route to ergodicity is by controlling the usual
configurational and kinetic temperatures along with the $2^{\text{nd}}$ order
configurational temperature. For the BT thermostat, controlling the usual
configurational temperature along with the $2^{\text{nd}}$ order
configurational temperature is sufficient to make it ergodic. Our method also
provides a new ergodic generalization of NH thermostat that reduces to kinetic
moments method for a single harmonic oscillator.
