gnuplot seems to be able to do contour plots: http://www.gnuplot.info/. Many open source coding platforms have sophisticated plotting libraries: for example, R has ggplot and Python has matplotlib.
Gnuplot is quite elaborated tool in creating high quality figures if all kinds. Python is very good to. Online, there is plenty examples avaiable for both approaches. Just choose what is more convenient for you.
I used both. Gnuplot can be automatized in the form of shell scripts in Linux. Python can be written in the form of programs.
When you need to produce many figues of the ame kind from different datsla, scripts are the way to go.
Ocean Data View (ODV, https://odv.awi.de/) & Generic Mapping Tools (GMT, https://www.generic-mapping-tools.org/) are classic freeware used by geoscientists.
I guess it depends on what you're generally using.
If you're familiar with MATLAB (https://de.mathworks.com/products/matlab.html) or the free version of it, Octave (https://www.gnu.org/software/octave/download), then a depth-x-time plot as you mention would probably be a Hovmöller diagram. This type of diagram is quite easy to plot as you just have to interpolate the data for your desired spatial and temporal resolution with " 3D meshgrid" and then plot the variables using "contourf".
If you're using python, here is a great example with the entire script available: https://unidata.github.io/python-gallery/examples/Hovmoller_Diagram.html
Otherwise if you just want a 3D Scatter Plot, there are again tutorials for MATLAB (https://de.mathworks.com/help/matlabmobile/ug/creating-3d-scatter-plot.html)
or Python and Matplotlib (https://pythonprogramming.net/matplotlib-3d-scatterplot-tutorial/).