Acclimation is a big help. Coming out of winter in Wisconsin (gets to -20 F), a 30-40 degree rainy commute this time of year is not as bad as it is in the fall. I recommend cold showers to get used to the feeling ;).
You should have something on the outside to at least block the wind. This minimizes the "cold wind + soaked clothes" death effect. Mostly waterproof jackets and pants truly are a treat, but I've been drenched in a cold rain plenty of times with an awful "rain jacket" to know that having something to at least block the wind is key.
Good underlayers also help. I always use a fishnet base layer on my upper body (Bryne is the brand) and some kind of wool or synthetic sweater over that. Double or triple layer of real wool socks and mittens (with shoes and overmitts that block the wind). The wet takes a lot out of you, so don't feel shame in overdressing.
Eat more food at more frequent intervals than normal to keep your body fueled and able to generate heat.
I sort of jest with the statement, "gotta get used to it," but honestly, that is what you have to do as there is no such thing as warm and dry during a 35 degree rain. Days like those make the sun feel extra glorious!