Not a great idea, but not for the caffeine quantity that others mention (though perhaps for that, too). Espresso is meant to be drunk quickly and hot. Even the glasses are designed to keep the surface area minimal and give the drinker control over how (minimally) cool they allow the espresso to get.

Keeping a large amount in a mug for a while will allow bitter notes to develop and will mute the creamy and sweet notes/feel that make espresso worthwhile. You can minimize that a bit by diluting the coffee (a 3-hour old latte or americano changes less than a straight shot would in the same span), but it'll still change.

Pour over is really the only method that is intended to be drunk at varying levels of heat, and you can make it super strong if that's what you're looking for.