Converting electricity to heat is an extremely easy process. All that is necessary is to provide a path for current to flow in such a manner that (1) the amount of current will not overload the source, and (2) the device's equilibrium temperature where it dissipates as much heat as its generates is low enough that the device doesn't self-destruct.
Suppose one has three boxes, one of which contains a 15 watt heater, one of which contains a 15 watt incandescent bulb, and one of which contains a 15 watt LED bulb, and feeds 15 watts of power to each bulb. In the first box, the heater will impart 15 joules of heat energy to the surrounding air each second. In the second box, the incandescent bulb might impart 7.5 watts of heat energy to the surrounding air, release 7 watts of infrared radiation, and 0.5 watt of visible radiation (light). The 7.5 watts of released radiation would then get converted to heat when it strikes the inside of the box. In the last box, the bulb might impart 5 watts of heat to the surrounding air and release 10 watts of visible radiation (light), which would then get converted to heat when it strikes the inside of the box.
In all cases, 15 watts of electrical energy would get converted to 15 watts of heat inside the box. The lights would first convert the energy into some other form that could serve some other useful purpose before it gets converted into heat, while the heater ignore the opportunity to do something useful with the energy in addition to producing heat.
The biggest caveat with using a "1000 watt" computer as a 1000-watt heater is that purpose-designed heaters are designed on the assumption that if they are below a certain temperature, they should convert 1000 watts electrical energy to heat without regard for whether everything useful they do besides produce heat (e.g. lighting up a temperature display) could be done with less than 1,000 watts. Computers, by contrast, are designed on the assumption that if they could serve all of their useful purposes besides producing heat while consuming less than the nameplate amount of energy, they should do so.
Additionally, any device which markets itself as a "1000 watt" heater would be expected to be able to dissipate 1000 watts of heat continuously without overheating. By contrast, a "1000 watt" computer would merely guarantee that it wouldn't consume more than 1,000 watts, and not necessarily guarantee that it would be able to continuously dissipate 1,000 watts without overheating. A properly designed computer should be designed so that if it starts to overheat, it will reduce its power consumption sufficiently to prevent damage, but such power reduction would limit the computer's usefulness as a heater.