Is there a point where further dilution of ethanol is not exothermic? Diluting concentrated ethanol with water is exothermic. Diluting 95% refined spirit into 40% vodka makes the resulting product definitely warm. Dilution of 60% absinthe with water that is cool, but warmer than "nearly freezing" results in a lukewarm, unappetizing drink. I haven't noticed the effect when diluting weaker alcohols though.

Is there a threshold of concentration where further dilution of water-ethanol mix doesn't produce heat? Or is it merely an asymptotic relation, where at lower concentrations the effect becomes hard to notice?
Mixing ethanol and water is exothermic all over the range at about room temperature. Data are available, e.g., here excess enthalpy ethanol-water

However, at relatively high temperature and at least around azeotropic composition,  the mixing should become endothermic otherwise the ethanol-water azeotrope should boil at higher temperature instead of having Bp of 78.1 °C.