It looks like rain-soaked Reykjavíkers may actually enjoy some dry weather over the next few days. According to the weather maps on the Icelandic Met Office website, no precipitation is expected in the capital area through the weekend.
Although it will likely be overcast in the capital on Thursday and Friday during the day, Reykjavík residents—and indeed people all over Iceland—may very well see sunny skies on Friday evening after 6:00 PM. Temperatures look like they will mostly hover around 6° – 7° C [42.8° - 44.6° F], although the temperature may jump to 10° C [50° F] on Sunday afternoon.
This May has been the rainiest on record for Reykjavík since 1989. That year, the city saw 126 millimetres of rain during the month, while as of this week, it has received 127.8mm.