Its roughly 3.41 BTU per watt, so assuming you have a 500 watt total draw (measured at the wall) for the system you would be generating an extra 1,705 BTU/hr in heat. Simply use the AC room size recommendations and get one 2,000 BTU watt higher using this example. Here is a AC sizing guide for various room sizes:
http://www.apartmenttherapy.com/what-size-air-conditioner-do-i-need-191400So say you have 600 sq ft of apartment space to cool down, they recommend a 14,000 BTU unit. Then add your mining overhead to this using 3.41 watts/BTU mentioned earlier, so using the 500 watt system example, you would want something in the 16,000 BTU range. Also make note of that sites recommendations if your apartment gets a lot of sun, or if it will have additional people, as these factors will also add additional capacity requirements.