We have studied high-resolution angle-resolved photoelectron energy distribution curves from Cu(100) and Cu(111) in the temperature interval 38 less-than-or-equal-to T less-than-or-equal-to 700 K. For several well defined peaks, originating from bulk direct transitions as well as from surface states, we determined separately the temperature dependence of emission amplitude, peak area and peak width, respectively. Our results clearly demonstrate that the description of thermal effects in angle-resolved photoemission spectra by the definition of a Debye-Waller factor with an adjustable Debye temperature is not adequate.