What kind of data would one need to prove that a particular city has become hotter over the last few decades?
Average temperatures over the decades.
To say a particular place has become hotter or cooler, one would need the average temperature of that place over few decades. Thus one can have data of temperature, recorded on a particular day every year or every two years over the decades. By analysing such data (using tools like tables, graphs, average etc), one can prove the change in the climate of a particular place.