Spreading and solidification of liquid droplets are elementary processes of relevance for additive manufacturing. Here we investigate the effect of heat transfer on spreading of a thermoresponsive solution (Pluronic F127) that undergoes a sol-gel transition above a critical temperature Tm. By controlling the concentration of Pluronic F127 we systematically vary Tm, while also imposing a broad range of temperatures of the solid and the liquid. We subsequently monitor the spreading dynamics over several orders of magnitude in time and determine when solidification stops the spreading. It is found that the main parameter is the difference between the substrate temperature and Tm, pointing to a local mechanism for arrest near the contact line. Unexpectedly, the spreading is also found to stop below the gelation temperature, which we attribute to a local enhancement in polymer concentration due to evaporation near the contact line.