We discuss gamma-ray bursts (GRBs) that have very hard spectra, consistent with blackbody radiation. Several emission components are expected, on the basis of theoretical considerations, to be visible in the gamma-ray band, mainly nonthermal emission from cooling, relativistic electrons and thermal emission from a wind photosphere. We find that the pulses we study are consistent with a thermal blackbody radiation throughout their duration and that the temperature kT can be well described by a broken power law as a function of time, with an initially constant temperature or weak decay (~100 keV). After the break, most cases are consistent with a decay with index -. A few of the pulses have a weak nonthermal component overlaying the thermal one and are better fitted with a combination of a thermal and a nonthermal component. We further demonstrate that such a two-component model can explain the whole time evolution of other bursts that are found to be thermal only initially and later become nonthermal. The relative strengths between the two components vary with time, and this is suggested, among other things, to account for the change in the modeled low-energy power-law slope that is often observed in GRBs. The secondary, nonthermal components are consistent with optically thin synchrotron emission in the cooling regime. We interpret the observations within a model of an optically thick shell (fireball) that expands adiabatically. The slow, or absent, temperature decrease is in the acceleration phase, during which the bulk Lorentz factor increases, and the faster temperature decay is reached as the flow saturates and starts to coast with a constant speed. We also discuss a Poynting-flux model, in which the saturation radius is reached close to the photosphere. Even though these observations cannot tell these models apart, the latter has several attractive advantages. The GLAST satellite will be able to clarify and further test the physical setting of similar thermal pulses.