A very curious question indeed!
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.