Display result (image) of computation in website
Save the image to a file. Return a webpage that contains an <IMG SRC=...> element. The SRC should be a URL pointing at the file.
For example, suppose you save the image to a file called "temp2.png" in a subdirectory called "scratch" under your document root. Then the IMG element would be <IMG SRC="/scratch/temp2.png"> .
If you create and save the image in the same program that generates the webpage that refers to it, your server won't return the page until the image has been saved. If that only takes a few seconds, the server is unlikely to hang. Many applications would take that long to calculate a result, so the people who coded the server would make sure it can handle such delays. I've done this under Apache, Tomcat, and GoServe (an OS/2 server), and never had a problem.
This method does have the disadvantage that you'll need to arrange for each temporary file to be deleted after an expiry period such as 12 hours or whenever you think the user won't need it any more. On the webpage you return, if the image is something serious that the user might want to keep, you could warn them that this will happen. They can always download it.
To delete the old files, write a script that checks when they were last updated, compares that with the current date and time, and deletes those files that are older than your expiry period. 
You'll need a way to automatically run it repeatedly. On Unix systems, if you have shell access, the "cron" command is one way to do this. Googling "cron job to delete files older than 1 hour on web server" finds a lot of discussion of methods.
Be very careful when coding any automatic-deletion script, and test it thoroughly to make sure it deletes the right files! If you make your expiry period a variable, you can set it to e.g. 1 minute or 5 minutes when testing, so that you don't need to wait for ages.
There are ways to stream your image back without saving it to a file, but what I'm recommending is (apart possibly from the file deleter) easy to code and debug. I've used it in many different projects.
I have a python script that generates a heightmap depending on parameters, that will be given in HTML forms. How do I display the resulting image on a website? I suppose that the form submit button will hit an endpoint with the given parameters and the script that computes the heightmap runs then, but how do I get the resulting image and display it in the website? Also, the computation takes a few seconds, so I suppose I need some type of task queue to not make the server hang in the meanwhile. Tell me if I'm wrong.
It's a bit of a general question because I myself don't know the specifics of what I need to use to accomplish this. I'm using Flask in the backend but it's a framework-agnostic question.