I believe it was le temps before, yet now it is les temps
Maybe I've gone crazy, but I've thought that it was le temps previously ...
The weather is always "le temps", singular. Time is a bit harder but similar to English. "Le temps qui passe", the time which passes, singular. For particular periods, e.g. "les lemps anciens", ancient times, plural as in English. The only exception that I know, but there may be others, is "le bon vieux temps", singular, where I would use "good old timeS", plural, in English. Hope this helps.
Yes, "les temps" can mean "the times" in the sense of a period of time. "Les temps modernes" - modern times, "les temps difficiles" - the hard times.
I would use "fois" or "reprises" to translate "times" when it means separate occasions. (I don't remember ever hearing "plusieurs de temps" but there is "en plusieurs temps", meaning in several time periods, or by stages.)