Getting the town you were besieging to do the right thing and surrender could be a long and tiresome exercise. Disease and hunger were just as likely to affect the besiegers as those within the offending walls.
Often to hurry things along, the army camped outside would resort to a range of terror tactics. This could include, as has been documented, decapitating the last messenger to arrive with the peace terms then nailed to his head and catapulted back over the walls. A pretty clear response.
Fire was always a good tactic. Plenty of buildings within the fortifications would have thatched or wooden roofs including the Great Hall. Large quantities of hay might also be lying around in bales which could ignite with ease. All that was required were arrows dipped in flaming pitch or jars of the stuff hurled over.
More ingeniously, I’ve read of animals being smuggled through sewers and other openings in to the town with flaming material attached behind them on a rope – or even attaching a small flaming object to a bird in the hope it would land on a thatched roof.