In this paper, specific features of operation of the calorimeter of the IHEP-JINR Neutrino Detector on the basis of liquid scintillation counters upgraded for time of flight particle identification are described. Data acquisition system, algorithms of response reconstruction, and calibration of calorimeter counters are described in detail. Estimate of time and spatial resolution of counters is obtained on tracks of vertical cosmic muons. The averaged time resolution is σ = 1.2 ns, and the coordinate resolution is σ = 13 cm.