You can understand "par un temps si beau" by the sentence "by a such beautiful time". We have a such great weather today in Paris as you told it that I have to confess you the thing, during less a second, I was asking myself if you were there in Paris for asking that^^ Indeed, it's at your location that you've throughout the year a such beautiful weather ;))

Eventually you could use "avec", e.g: "avec un temps pareil, il serait impensable de rester enfermé chez soi". Or then you could also use a second clause, like in "personne ne veut rester enfermé chez soi, quand il fait si beau dehors" or "tandis qu'il fait si beau dehors". But "par un temps si beau" sounds good and it's short, so I think it will be preferred in spoken French.