Yes. This is sometimes called "Carnot tax".

The efficiency of any heat engine is bounded by the Carnot cycle. In simplified form, it depends on the temperature differential between the cold and the hot parts. So if your hot part is at 300C (572 Kelvin), and the cold part is at 30C (300 Kelvin) then the absolutely best possible efficiency is around (572-300)/572*100% = 47%.

You see that it quickly becomes inefficient as the differential goes down. E.g. if you use 90C to store the heat, then the maximum efficiency is just 17%.