When I went in June 2003, I had one night below freezing near Chita.
Average May temp. in Wakkanai, the northernmost city in Japan, is 8.7 degrees C.
But really your choices are either wait for the Sakhalin ferry on June 8 (and enjoy more of Japan

), go to Vladivostok (nice group of bikers

, unpleasant customs house

), go to Korea (extra ferry ride, sometimes hard to get a one-way ticket from Japan

), attempt to hitch a ride on a fishing boat (not sure if legal

so Japan customs may not stamp out your carnet).