Current through a resistor exhibits temperature-dependent white noise fluctuations called Johnson-Nyquist noise. For a 2D electron system, measuring the magnitude of these fluctuations provides a direct measurement of the electron temperature and enables methods for inferring specific heat and thermal conductivity. Here I show how to understand Johnson noise both for electrons whose flow is dictated by Ohm's law and for electrons whose flow is hydrodynamic. I then discuss experimental results from the group of Philip Kim, which use Johnson noise measurements to demonstrate a novel method for inferring specific heat and thermal conductivity for arbitrary materials and quasiparticle excitations. Experiments in the Corbino geometry also reveal a novel, qualitative signature of hydrodynamic flow without the need for nonlocal measurements.