Stopping services is not necessary - with linux, you can delete files that are still open, and they will only really be removed from disk & the space recovered when the last access handle to the file is closed.
As files in /tmp, by definition, aren't guaranteed to be persistent, it should not break anything if you just remove everything. But to be safe, you can use the suggestion to use find with option -mtime +1 to get only files older than a day, and then let it remove them with -exec rm -rf {} \;. Note that if you don't understand how this works you probably shouldn't use it, as there is ample opportunity to introduce bugs that sooner or later do a rm -rf /, wiping your system.