To know if a fuse is blown in the box, you can visually inspect the fuses. A blown fuse will have a broken or melted filament, which can be seen through the transparent part of the fuse. Additionally, you can use a multimeter to test the continuity of the fuse. If the multimeter does not show continuity, the fuse is blown.
A blown fuse can cause heat not to work if the fuse is part of the circuit that controls the heat. For example, if the fuse for the furnace fan is blown, the fan will not be able to circulate hot air throughout the house. As a result, the house will not be able to stay warm.