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I prefer to drink coffee cold. So, after the coffee is done brewing, I leave it to rest for some time and drink it later.
Will the coffee lose its strength, if it is cooling down?
Yes, but not in any significant or noticeable amounts. Caffeine is stable in solution for quite some time. Considering a average cup of coffee (~100mg of caffeine), you may lose a few milligrams of caffeine over an extended rest period. Given that caffeine content varies in any given cup of coffee (many sources list variations as wide as 60mg to 200mg, or more) you are unlikely to notice any difference in the caffeine content.
What you may notice is a difference in the taste. They are many suggestions out there on how to cold brew coffee. It may be worth your time to research an alternate brewing method.
Largest drops observed after a 24 hour period were 4.1% during this study: https://www.ncbi.nlm.nih.gov/pubmed/2500782