There will always be some degree of heating. In the best of cases,
it won't be noticeable, but that heat is from losses, and there's
always 'some'. In general, it sounds as if the tuner isn't tuned
correctly. The least amount of inductance necessary is a very good
idea! You might also check things in general, connections are good,
component 'size' is sort of at least in the 'ball-park', that sort of
thing. Keeping that feed line away from things is another idea.
Nothing 'extreme', just 'good sense'.
Not much help, but...
- 'Doc