I've done this route twice. Once this year
Epilogue | A bicycle ride across Africa and once in 2002:
Bicycling Reno to Salt Lake City, via US 50, "the Loneliest Road".
Cold Springs was open this year. My 2002 trip was at end of June and it did get warm on some afternoons - so starting early is definitely a good idea. The most challenging part in 2002 trip was Fallon to Austin so this year, I split this into two days with a stop in Middle Gate which made it a fair amount easier. The biggest gap I had both times was Eureka to Ely.
As far as water goes, I put some extra bottles and bags in my panniers and that seems to work well. While this route claims to be a "loneliest road", I've definitely seen more remote places - in which case I just added more water into my panniers; highest amount was ~18 liters in Northern parts of WA, Australia.