The paper describes a dry-cooled AC quantum voltmeter system operated up to kilohertz frequencies and 7 V rms. A 10 V programmable Josephson voltage standard (PJVS) array was installed on a pulse tube cooler (PTC) driven with a 4 kW air-cooled compressor. The operating margins at 70 GHz frequencies were investigated in detail and found to exceed 1 mA Shapiro step width. A key factor for the successful chip operation was the low on-chip power consumption of 65 mW in total. A thermal interface between PJVS chip and PTC cold stage was used to avoid a significant chip overheating. By installing the cryocooled PJVS array into an AC quantum voltmeter setup, several calibration measurements of dc standards and calibrator ac voltages up to 2 kHz frequencies were carried out to demonstrate the full functionality. The results are discussed and compared to systems with standard liquid helium cooling. For dc voltages, a direct comparison measurement between the dry-cooled AC quantum voltmeter and a liquid-helium based 10 V PJVS shows an agreement better than 1 part in 1010.