Firstly backup everything important to a different HDD.
If it only works properly when it's cold, get an external exclosure, or better still, just a USB->IDE/Sata cable & stick a fans to blow across it.
Lets you connect & disconnect until you get everything you want off it
1) 38degC is fine if not lower than most people HDD's.
2) Yes, a small gap restricts airflow & prevent heap from escaping, but except in extreme cases, the airflow should still be sufficient - how much room? 5mm, 10mm's - 1mm?
3) Sure, why not - it probably won't make much difference if you system has 1/2 decent ventilation anyway, but it won't make it any worse - but if you only have a small gap anyway .. if might not make any difference.
Unfortunately .. HDD's are made to fail these days - in a work situation, I wouldn't recommend using any mechanical HDD for more than 3 years - in a personal environment .. depends on how much you use the HDD.