Abstract: Thermionic cathode is widely used in accelerators, FELs and all kinds of vacuum electronics. For better performance and long stable running, low emittance with notable contribution from cathode is needed. Emittance of perfect thermal cathode only depends on radius and temperature. However, emission non-uniformity exists due to cathode surface profile, material distribution, temperature variation, crystal orientation, etc., which may cause intrinsic emittance growth, brightness decline, envelop size augment, device performance deterioration or even failure. To understand how intrinsic emittance is manipulated by temperature variation, a general intrinsic emittance model consisting of contributions from surface non-uniformity is developed based on general thermal emission. Numerical calculation for a cathode with radial temperature variation shows that RMS emittance declines about 15% when non-uniformity reaches 10%, which well conforms to FDTD-PIC simulation result.