Questions about I.V.-caused thrombosis

I have two bumps on my forearm in my vein. My cardiologist told me it was “thrombosed” (his word) vein caused by an I.V. and to put some hot compresses on it.

My understanding of the word is that it means blood clot.

I asked him if I needed to be concerned, and what would happen if they broke off? He said I wouldn’t even notice something that size.

Now, he is a cardiologist and seems competent, so I trust I am in no danger, but now I have some questions.

Searching for thrombosis I can only find stuff on “deep-vein thrombosis” and nothing on I.V.-induced thrombosis. So here are my questions:

  1. What do the hot compresses do?
  2. How big of a clot does one have to worry about? Why am I in no danger? (Again, I trust that I’m not, I just find it interesting and want to know why some clots are dangerous and others aren’t)