Spicules of the so-called type II were suggested to be relevant for coronal heating because of their ubiquity on the solar surface and their eventual extension into the corona. We investigate whether solar spicules are heated to transition-region or coronal temperatures and reach coronal heights ({≫} 6 Mm) using multiwavelength observations of limb spicules in different chromospheric spectral lines (Ca ii H, Hɛ, Hα, Ca ii IR at 854.2 nm, He i at 1083 nm) taken with slit spectrographs and imaging spectrometers. We determine the line width of spectrally resolved line profiles in individual spicules and throughout the field of view, and estimate the maximal height that different types of off-limb features reach. We derive estimates of the kinetic temperature and the non-thermal velocity from the line width of spectral lines from different chemical elements. We find that most regular, i.e. thin and elongated, spicules reach a height of at most about 6 Mm above the solar limb. The majority of features found at larger heights are irregularly shaped with a significantly larger lateral extension, of up to a few Mm, than spicules. Both individual and average line profiles in all spectral lines show a decrease in their line width with height above the limb with very few exceptions. The kinetic temperature and the non-thermal velocity decrease with height above the limb. We find no indications that the spicules in our data reach coronal heights or transition-region or coronal temperatures.