After the quest, Battle for Whiterun, Heimskr's House sustains major roof damage, and debris in front of the door makes the house inaccessible for the remainder of the game. Heimskr will then take up residence in the nearby inn, The Bannered Mare, and continues his rants every day at the shrine of Talos next to his house.
Oddly, there are many skulls laying around the house.
Even though the house becomes inaccessible after the Battle for Whiterun, the door can still be activated while standing in a certain position in the debris. Activating it will do nothing but change the activate text from 'open door' to 'close door', similar to an iron door or wooden door in a crypt, cave or tomb.
PC 360 PS3 If a Thieves Guild small job targeting this house is accepted after completion of Battle for Whiterun, it will be impossible to complete, as the house cannot be entered. PC players may type "coc whiterunheimskrshouse" into the console, you will then be teleported into the house and it will still be intact.