We propose two new thermostats which can be employed in computer simulations to ensure that two different variants of the configurational temperature fluctuate around their equilibrium values. These new thermostats differ from one previously introduced by Delhommelle and Evans [Mol. Phys. 99, 1825 (2001)] in several important ways. First, our thermostats are derived in the same spirit as the Nosé-Hoover thermostat and therefore generate the canonical phase-space distribution. Second, our thermostats involve simpler equations of motion, which do not involve spatial gradients of the configurational temperature. They do not suffer from problems stemming from stiff equations of motion and furthermore, in large temperature perturbation simulations, the measured temperature follows the set-point temperature without any overshoot, and with good damping of oscillations. We show that both of our configurational thermostats are special cases of a more general set of Nosé-Hoover equations proposed by Kusnezov et al. [Ann. Phys. 204, 155 (1990)]. The new thermostats are expected to be highly useful in nonequilibrium simulations, particularly those characterized by spatial inhomogeneities. They should also find applicability in simulations involving large changes in temperature over small time scales, such as temperature quench molecular dynamics and radiation damage modeling.