flycheck-mode creates temporary files in the current directory. That is annoying. How can I disable/set the default place for these temporary files.
TL;DR: Update to the latest Flycheck release to get rid temporary files entirely.
You cannot change the directory Flycheck writes its temporary files to. Flycheck tries hard to avoid writing to the current directory, and normally uses the system's temporary directory. But when it writes to the current directory it does so for a reason. In ESLint specifically that's because eslint uses the filename to locate its configuration files, and moving the file out of the source code tree broke user's eslint configuration.
However, since Flycheck 0.25.1 Flycheck passes buffer contents on standard input to most syntax checkers, including eslint. Flycheck creates no temporary files for these checkers anymore which should solve all issues with tools that watch the source code tree.