My understanding of most remoting technologies is that you are sending mouse and keyboard commands and retrieving compressed video / images. I'd be amazed if most viruses had the capability to come across via remoting.
However, if you are doing a lot of data transfer from the infected machine then there is greater risk.
One thing to do is to make the connecting machine is bulletproof. Make sure you've got your malware, virus scanner and firewall all in place. Then connect over.
I couldn't see if TeamViewer supported Ubuntu. But if it does you could boot into a Ubuntu live CD, install TeamViewer and do your remoting. The live environment is only temporary so it doesn't matter what happens.
Thanks for your input.
I definitely wouldn't be doing any data transferring with the infected computer.
I ended up fixing the problem live being in front of the computer that had malware, but I was just wondering since I use TeamViewer fairly consistently.
the only real threat over a network is a worm they will actively seek a network connection so they can spread. things like trojans and viruses need a host program to spread so as long as your not swapping data your reasonably safe from them.