Attosecond (asec) X-ray free-electron laser (XFEL) has attracted considerable interest over the past years. Nowadays typical XFEL application experiments demand 1010-1011 photons per pulse, which corresponds to a peak power of terawatts (TW) in case of asec hard X-ray pulse. To the realization of such TW asec-XFEL pulse, however, the unavoidable increase of slice energy spread (SES) due to laser heater, which is commonly used to mitigate the micro-bunching instability (MBI), would be a major obstacle. To deal with this problem, the effect of such a SES is investigated in this work. The results reveal that (1) SES of a current spike is linearly proportional to the peak current of a current spike in an electron beam, (2) surprisingly, this linearity is independent of the wavelength of an energy modulation driving laser which is used to make a current spike and (3) the gain length of current spike in the undulator is sensitive to the initial SES, so there is an optimal peak current of the current spike for successful FEL lasing process. Utilizing these characteristics, a series of simulations with parameters for Pohang Accelerator Laboratory X-ray Free Electron Laser was carried out to demonstrate that an isolated, TW asec-XFEL pulse can be generated even when the SES is increased due to the usage of laser heater to prevent the MBI in the XFEL. We show that an isolated X-ray pulse with >1 TW and a pulse duration of 73 as (~3 × 1010 photons/pulse at 12.4 keV or 0.1 nm) can be generated by using ten current spikes with optimal peak current. It becomes clear for the first time that the disadvantage from the increased SES can be indeed overcome.