I haven't spent the night at 13,000 but I've been many summer nights at 8,000-11,000. You often get frost in a water bowl or puddle on a clear night any summer month. So 35F is to be expected. A cold front, then no wind and a clear night and you could have 25F at 10,000'.
An incredibly useful bit of thermodynamic data is that when air expands, it loses 3.5F for every 1000 feet of elevation rise*. A high of 100F in Fresno means 100-(4x3.5) = 86F in Yosemite Valley at 4,000'. Afternoon high on Half Dome at 9,000' = 100 - (9x3.5) = 69F. If there's any air movement, this is accurate to within just a few degrees.
So extrapolating from my 10,000 foot experience, subtract 10F for 13,000 feet. Expect 25F, be prepared for 15F. The bigger issue is you could have 30F but 50 mph at 13,000 feet. Plus rain or hail. That's a tougher survival situation.
Be ready to change your plans, especially if you're going light. You can sometimes drop 5,000 feet in 2-3 hours, increase 17F, get out of the wind and into the shelter of trees.
*This is referred to as adiabetic expansion. Because of humidity, rainfall and increased solar input, while I use 3.5F/1000' on the upwind side (western side of the Sierra), the air increases 5F/1000' going down the other side.