The influence of heating rates and annealing temperatures on the transition temperatures (Tc) and critical current densities (Jc) of pure MgB2, carbon nanotube- and nano-SiC-doped in situ monofilamentary MgB2/Fe wires was investigated. It was found that higher Jc was obtained for pure MgB2 samples when heat treated with slower heating rates. SiC-doped samples also have higher Jc with slower heating rates, but the Jc is less sensitive to annealing temperatures. However, the Jc of the carbon nanotube-doped wire was found to be insensitive to heating rates. The variation in Tc and Jc with heating rate, and the different behaviors of differently doped MgB2/Fe wires, make it essential to carefully select the optimum heating rates for heat treatment.