I'm planning on buying this card: http://www.newegg.ca/Product/Product.aspx?Item=N82E16814150632
But I don't have liquid cooling on my current build, would this card still run okay and not burn out within a few months of use?
These cards usually have really good cooling, especially on a card of this caliber as long as you have fans for your other parts in your system you should be fine. Your card should never go above 75+ degrees celsius under full load as long as its below that that's a safe threshold they can handle 80+ usually, but as a rule of thumb 75 or less is the way to go for full load.
Hope this helped.