If you have a user interface program for the probe then you could use VNC to remotely view the remote machines desktop
http://www.uk.research.att.com/vnc/
But that's not how I would do it I would try to figure out how your temperature probe presents it's data to the serial port, do you have detailed information on this bit ?
Does it for example simply output a continuous data stream with the temperature info or do you have to poll it somehow in order to request the current temperature.
One quick and dirty way would be if it presents a continuous data stream then it is fairly trivial to write a short script to cat /dev/ttyS0 (or whatever port you have it on), reformat the data (if required),write the finished data to a text file, wait (a short amount of time) and then repeat.
Then simply use Apache to publish the text file (after your script has perhaps padded it with a bit of html like adding the refresh meta tag so that the browser viewing the page keeps reloading it ) Job Done !
You could even add another script to monitor the dial up connection and reconnect if something causes the connection to drop.
Wayne