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This paper gives a numerical model to deal with the thermal effect of field-induced thermal-assisted current passing through the microprotrusion on the cathode surface of a planar high-voltage vacuum diode. The model of protrusion is based on a one-dimensional truncated cone, whose physical and thermal properties have been assumed temperature dependent. The influences of space charge effect and Nottingham effect are included. According to the simulations, the delay times of explosive electron emission of cathodes made of different materials are given and compared with the experimental results, which seems to be in agreement.