If you’re sick of going back and forth from Thunderbird to Firefox or IE, then the ThunderBrowse extension is what you need. It basically creates a mini browser within Thunderbird so that you can view links sent to you via mail within Thunderbird itself.
It doesn’t modify your toolbar in anyway because it adds the URL bar to the windowpane of the e-mail message you are reading. Just cut and paste the link into it and the mini browser will take you straight there. It’s not advisable to use this if your eyesight is bad – the graphics and text can be hard to decipher, although you can select a full-screen mode. Failing that you can simply right-click and select to open the link in your custom browser.
There’s also a ton of customisation options for hotkeys which can be configured by typing ‘about:commands’ in the URL bar. This is such a good extension that it should be bundled as standard in the next release of Thunderbird. You’ll save both RAM and productivity reading links within it rather than outside of it.