Sirius Black was certainly rubbing off on him.
He would never have been so unpractical as to be caught out in the middle of Muggle London, in the pouring rain, without an umbrella. No way to whip out his wand and spell himself dry. No safe Apparation points close by... No choice except to just suck it up and walk, soaking wet, for blocks until he found the closest wizarding neighborhood.

Remus Lupin muttered an off-handed comment about Sirius Black and his perpetual devil-may-care attitude about life. But a smile was already teasing at the corner of his mouth. He shivered a bit, only partially because of the rain. The rest of the reason might have had something to do with the mental image he suddenly had of Sirius, his dark hair dripping from the rain, his grey eyes like the storm clouds -only full of laughter...

Suddenly it was very, very important to be back at the little flat they shared as fast as possible. Short of Apparating... Remus tossed his eyes around crazily - ahh, ha! -- he grabbed a loose Muggle newspaper from the top of some dustbins. Headlines about events he didn't know about, didn't care about. Looking around serruptitiously, he whispered a quick Impervious and then hoisted the newly-water-proof paper above his head.

He probably looked just like a fool; a fool in the rain. A fool on the wrong block.
And he began to trudge merrily back toward his home, where Sirius was most certainly waiting for him.