Macbook pro 13 mid 2010 external monitor
Your Macbook supports an external monitor with a max resolution of 2560x1600. It will be fine, for better performance, close the lid so that there is only 1 display open.

I had 2x Thunderbolt displays at 2560x14400 (13" Late 2011) and was only experiencing slow movements after I plugged in the 2nd display. 1 will run just fine. :)