Dikes beginning to propagate away from a magma source are thin and grow slowly, and thus are susceptible to freezing. A self-similar solution is obtained for a dike propagating down a temperature gradient when the wallrock and magma temperatures are equal at the chamber wall. The solution applies only to the special case of a single-component magma intruded at the solidus temperature, but provides insight into the case in which the magma temperature is above the solidus. The dike propagation velocity, relative to that in the absence of freezing, is determined by a single dimensionless parameter β. For β sufficiently large, magma freezing chokes the dike faster than propagation can elastically widen it, and the dike cannot grow. If the magma intrudes at a temperature above the solidus, there is some value of β above which the dike will propagate a certain distance and freeze, and below which it will propagate until depletion of the source or three-dimensional elastic effects promote freezing. For reasonable parameters this process can explain why basaltic dikes are found far from obvious source regions, while granitic dikes are scarce except in the immediate vicinity of granitic plutons. Even if a rhyolite is 5 orders of magnitude more viscous than a basalt, however, this distinction can be offset if the rhyolite has an excess source pressure only 1 order of magnitude greater than that of the basalt.