"Does the current heat wave have anything to do with climate change?"
Let’s first distinguish what we mean by climate versus weather. Climate is the long-term average condition that tells us what types of clothing we should have in our closet during any given time of year at a particular location. Weather, in contrast, defines whether or not we should take an umbrella or raincoat to work on a particular day.
By that definition we would consider the recent heat wave as "weather," and its direct relationship to climate change is, therefore, tenuous. The recent heat wave was characterized by record-setting high dew point temperatures, along with higher than normal nighttime low temperatures. In the Duluth area during the week of July 18 - 24, the high temperature was 92°F, and the weekly average was 71.6°F. This was 5.4 degrees higher than normal for the period 1981 - 2011. Numerous long term records were set across the state during that period for the highest dew point temperatures, which were the result of the extremely high humidity we experienced.
However, the more appropriate questions in this context are: Relative to the long term average for our region: are the number and intensity of heat waves increasing? Are the dew points increasing? Are minimum nighttime temperatures increasing? The answer to these questions is generally "yes." The climate is changing, but we cannot specifically link individual weather events, such as a heat wave, to the phenomenon we know as climate change.
For those who enjoy looking at weather and climate patterns, a fun web site to explore is: http://mrcc.isws.illinois.edu/cliwatch.