Noncritically phase-matched (NCPM) fourth harmonic generation (FHG) of Nd:glass laser radiation in partially deuterated dihydrogen phosphate (KD*P) crystals has been demonstrated. At an Nd:glass laser wavelength of $1053.0\mathrm{nm}$ , NCPM FHG is achieved in 70% deuterated KD*P at a crystal temperature of $18.5\pm 0.1°\mathrm{C}$ . Tuning the fundamental laser wavelength from 1052.9 to $1053.2\mathrm{nm}$ , FHG in KD*P is NCPM by changing the crystal temperature from $17.9°\mathrm{C}$ to $20.5°\mathrm{C}$ . When driven with $2.4\mathrm{J}$ of second harmonic radiation in a $3\mathrm{ns}$ flat-top pulse, corresponding to $1\mathrm{GW}/{\mathrm{cm}}^2$ $2\omega$ drive intensity, $1.9\mathrm{J}$ of fourth harmonic radiation was generated in a $6\mathrm{mm}$ long KD*P crystal, yielding a second to fourth harmonic energy conversion efficiency of 79%.