Discrete data can only take a fixed set of values – e.g. shoe size, number rolled on a die, etc. Continuous data can take infinitely many values – e.g. height, length of time, temperature, etc. With a graph, in order for the graph to be continuous, you require both the x-axis and y-axis to have continuous data. So for this example, it depends how you plot it. The y-axis (temperature) is certainly continuous, but you wording for the x-axis (time) is ambiguous. If you are only dealing in whole numbers of minutes (e.g. the temp was measured once per minute) then your graph is discrete. If you are dealing with continuous time, then your graph is continuous.

Continuous means, well, exactly that, there’s no space in between, the line (or curve) continues – without being interrupted by space.