I have a napoleon 20" similar to the WSM, and I have briquette ash in the water pan, which is like using washed sand. When I do mine I use 12 briquettes to reach 100* in the cooking chamber. So I'm thinking you'll need around 14-16 to get to your 120* starting temp. I start them in a charcoal chimney, and dump them in the charcoal basket when they are mostly white on the outside. I should add that I always use kingsford blue bag (KBB); when I tried royal oak briquette, I had to use more than 12 to start. The air temp will also impact the amount of briquettes you need. With your heat wave you might not need as many.
Then to bump the temp up I start 6-8 more in the chimney, and add when lit. This takes practice, patience and a lot of baby sitting, especially the first few smokes; to get the feel of how much charcoal to start and when to add more. If you have any follow up questions post them, and I or someone else will try to answer them as well. Good luck and good smokin'.