I don't think its terribly warm in Budapest in the summer; and i'm sorry Ilja but I am not particularly concerned about global warming either Here are the stats: http://en.wikipedia.org/wiki/Climate_of_Budapest What I do have trouble dealing with (and I have been in Budapest in the summer and will be back this summer) is the lack of well engineered air conditioning. This isn't unique to Budapest, Europeans in general don't have the same concept of thermal comfort as do Americans.
Make sure you get accommodations with good A/C. If you rent an apartment, ask if it is built-in or a portable unit. If it is a portable unit you might want to look around a little more.
As for shorts. There is absolutely nothing wrong with a tourist wearing shorts. Locals going to the park or the bath house or something similar may also be wearing shorts, but generally speaking, in Budapest like in most of Europe the people dress a little more stylish than do we Americans.