Skew-T charts could be useful. Could work out approximate height from mb while dew point provides a measure of humidity - if I read the chart correctly.
According to this.
600mb = 14,000 feet
400mb = 25,000 feet
250mb = 36,000 feet
150mb = 46,000 feet
So this chart of 12pm today when there were short contrails suggests... judging by 500mb - 400mb level (20-25,000 feet), dewpoint was between -10C and -17C (the lower side). Presumably on Sunday the dewpoint was higher, so the water vapour from the jets did not have to cool so much to condense, because the contrails on that day were persistent. I don't know this though because I don't have skew-T plot from Sunday. I'll have to check another day to see if this works.