Are the strings new, or fresh..? Have you changed them..? If they are old (depends on usage, but over a year old I'd call 'old'...), they may be due for a change.
When changing strings, my tip is to be careful when winding onto the tuners to get the first wind near the bottom of the hole, then make sure that the next few winds start from the bottom of the post, crossing over the first wind. This helps block the winds in place. Once wound onto the tuner post (three or four turns is quite enough...), I tune the guitar up to pitch, lay the guitar on the bench (or table, or on the bed...), then take each string in turn and gently lift the guitar up by this one string. It's perfectly safe; the string won't break, but it will bed down at each end fully. I then tune up to pitch. Always tune 'up', never 'down' to the note. If the note is too sharp, tune down to flat and bring it back up.
I use any tuner (headstock, PC-hosted DAW, whatever, but cross-check with fifth-fret and octave harmonics from string to string. I start with the 'A' string, and check it again once all the others are done. It helps that I use Elixir strings, which hold their tuning much, much longer than others I have tried (for years I used Fender Bullets; Elixir now get my vote on all my guitars...).
I have never had a tuner (machine head...) issue, ever, on any guitar, vintage, old or new; maybe I've just been lucky. I'm not maniac, either, about tuning to 1% precision; fretted temperament inaccuracy is greater than that, anyway. I sound out my chords, and if they sound OK, the tuning is OK. The tuner is a guide, but it's one's ear that has the final decision, not the needle.
Yes, a decent set-up is always the starting point, and a competent guitar tech can do the job, but it would be very useful to learn the basics oneself (how to adjust intonation, String saddle height, check for neck bow, when (and when not...) to adjust a truss rod etc...). I doubt that the moderate temperatures we experience in these climes would affect tuning, or the guitar set-up, to any noticeable degree, but a set-up is always a good starting point. Better value than a set of tuners, anyway, as a first move.
Hope this helps.
Douglas