The creep-resistant casting nickel alloys (e.g., Inconel 713C) belong to the group of difficult-to-weld materials that are using for precise element production; e.g., aircraft engines. In precision castings composed of these alloys, some surface defects can be observed, especially in the form of surface discontinuities. These defects disqualify the castings for use. In this paper, the results of technological tests of remelting and surfacing by the Tungsten Inert Gas method (TIG) in an argon shield and TecLine 8910 gas mixture are presented for stationary parts of aircraft engines cast from Inconel 713C alloy. Based on the results of metallographic studies, it was found that the main problem during remelting and pad welding of Inconel 713C castings was the appearance of hot microcracks. This type of defect was initiated in the partial melting zone, and propagated to the heat affected zone (HAZ) subsequently. The transvarestraint test was performed to determine the hot-cracking criteria. The results of these tests indicated that under the conditions of variable deformation during the remelting and pad welding process, the high-temperature brittleness range (HTBR) was equal 246 °C, and it was between 1053 °C and 1299 °C. In this range, the Inconel 713C was prone to hot cracking. The maximum deformation for which the material was resistant to hot cracking was equal to 0.3%. The critical strain speed (CSS) of 1.71 1/s, and the critical strain rate for temperature drop (CST), which in this case was 0.0055 1/°C, should be used as a criteria for assessing the tendency for hot cracking of the Inconel 713C alloy in the HTBR. The developed technological guidelines and hot-cracking criteria can be used to repair Inconel 713C precision castings or modify their surfaces using welding processes.