Picosecond CARS spectroscopy and phased-locked schlieren imaging are used to measure time-resolved temperature and visualize compression waves in a diffuse filament, nanosecond pulsed discharge sustained between a pair of spherical electrodes in nitrogen and air at P=100 torr. The discharge generates stable plasma with high specific energy loading (up to ~0.5 eV/molecule), and with spatial dimensions sufficiently large to enable laser diagnostic studies. The results demonstrate that significant temperature rise, up to ∆T~200 K, occurs both in nitrogen and in air, on the time scale shorter than the acoustic time scale. The characteristic time for the rapid temperature rise in air, ~100 ns, is significantly shorter compared to that in nitrogen, ~1 µs. In air, a second significant temperature rise, up to ∆T~350 K, occurs on a time scale of ~100-500 µs. This "slow" temperature rise is almost entirely missing in nitrogen. Phase-locked schlieren images demonstrate a near cylindrical shape compression wave formed around the discharge filament, both in nitrogen and in air. An additional, near spherical shape compression wave is formed near the cathode, due to significant energy release in the cathode layer of the discharge. The compression waves, caused by rapid localized heating quantified by the present measurements, are similar to the ones produced by a surface nanosecond pulse discharge in atmospheric air used for high-speed flow control, where comparable temperature rise was detected previously.