Could you convince your landlord to look into treating the house with orange oil as an alternative? It's worth asking at least! We had this done at our house. It's totally non-toxic, you don't even have to leave the house, it's just as effective as tenting and in our case was half the cost!
Not sure where you're located, but just Google "orange oil termites" and your area, and you'll probably find a company that does it.
Here's an example: http://www.orangeoiltermitecontrol.com/