Related Q (especially its link to inversion): What is the relationship between altitude gain and temperature decrease when mountaineering?
This question is concerning the commonly used rule of thumb that an increase in elevation of 1000 feet will, on average, decrease the temperature by 3.3 to 5 degrees F (3.3 for moist air, 5 for dry). Some sources differ slightly in the exact numbers, but 3.3 and 5 are what I have seen most often.
I have read that local conditions on a mountain can trump this rule of thumb. Trying to understand this better, I found some examples of temperature increasing going up. I am wondering if this is a common occurrence or a rare one.
How closely can we trust this rule of thumb? Said another way: How often does reality deviate sufficiently from this rule of thumb to reduce its usefulness?
My specific example
I camped on Cascade Mountain in the Adirondacks at about 1500 to 2000 feet (460 to 610 meters) higher elevation than nearby Lake Placid. The temperature at Lake Placid was 37 F (3 C). One of the forest preserve stewards told me the next morning that she expected the temperature on the mountain to be below freezing.
This is not a huge elevation difference and perhaps not a great sample, but I am hoping to use it to help understand the conditions I was in and better prepare for future.
The mountain was wet below the tree line, so I would go with the lower change estimate.
Temp difference: 3.3 x 1.5 = 4.95 = approximately 5 F and 3.3 * 2 = 6.6 F, so...
Estimated temp: 37 - 5 = 32 F to 37 - 6.6 = 30.4 F
Estimate: 30 to 32 degrees F at my elevation. 27 to 29 F (about -1 to -3 C) if we use the 5 degrees per 1000 feet estimate.
Since it did not feel below freezing and I never noticed anything frozen or frosted, am I correct to assume that the rule of thumb was not accurate in our case and that it was not actually at or below freezing? I still am not sure how often the inaccuracies/inversions actually happen and am wondering if I can assume that it was the case in my situation.
In other words: what is the likelihood that the rule of thumb is not accurate? Is the likelihood high enough that we should always take the estimate with a grain (or more) of salt, or is the likelihood low enough that I should trust the estimate more than my gut based on how I feel?