Firstly, do not start video recording again, this will overwrite any remaining temporary file.
You may investigate what you can find in LapTimer's app folder using a tool like iExplorer.
The temporary file has been recorded to the LapTimer folder (Documents) in version 14.x LapTimer 15 will keep all files as long as they are not explicitly deleted. On the overheating: I'd suggest to place the iPhone somewhere you can point one of your air fans to. Another strategy is to reduce energy consumption - like screen brightness. Video recording seems to be a very energy intensive process, at least my iPhone gets pretty warm when recording for a longer time (independent of LapTimer or any Video app).