I assume you are talking about the ST10?
It's a loaded question. I can answer half of it. I do not know if the internals will suffer from having gravity "pull" things around: if the transformer is mounted on a PCB, it's different to have all the weight resting vertically than pulling sideways. This part, I wouldn't venture a guess.
The easy part to answer is heat dissipation: the ST-10 uses the top cover as a large surface that dissipates heat uniformly upwards. If you vertical-mount the unit, all the heat will move to the upwards side, and you could be concentrating the heat in a particular area which is not the original design. Still, it's rather cool and does not reach the extreme temperatures of class A/B or class A designs... but I'm not sure it's the best way to go.
A more technical confirmation from someone that knows the inner distribution better would be more useful, but I thought I'd share this concern.