If it makes you feel better about the SSD, you can add these lines to your /etc/fstab file:
none /tmp tmpfs defaults,noatime,mode=1777 0 0
none /var/tmp tmpfs defaults,noatime 0 0
none /var/spool tmpfs defaults,noatime 0 0
You could do the same with /var/log but you will never have a history of logged information because it will be lost every shutdown..
For browser or other user caches, there is a temporary user folder created at boot time at /run/user/nnnn, where "nnnn" is the user ID number, for example 1000 for the first user. You can make a directory there and set your browser to use that for the cache directory, according to the browser's settings for cache location. This cache will also disappear at shutdown, which may be a good thing for some users. ;-)