Extreme temperatures either very cold or very warm can have a negative impact, particularly if they are changing between temperatures regularly. Generally though, unless your display cabinet is directly next to a radiator, you should be fine.
Humidity is the real issue, as it can cause faux leather to crack and other materials such as rubber to perish. Again if you're going from high humidity to low humidity on a regular basis, this is the worst scenario.
What I did, was purchase a hygrometer for each of my cabs (ThermPro TP50)
It displays the current temp and humidity, and also records the extreme high and low reading for each. Fortunately, I have been within 'comfort' level for weeks now, so decided purchasing a dehumidifier was unnecessary. But it definitely helped put my mind at ease. Hope this helps!