Will an audio interface sitting on a tile floor have more background hiss than if it were placed on a table or stand?
I'll presume that you aren't talking about an "audio interface" but an "audio recorder". A mere interface may show reduced noise when in a cooled-down environment but the operating ranges of typical hardware are not close enough to 0K to make much of a difference.
Talking about the microphone, a placement near a tile floor will make a difference and will work best with pressure receivers, namely omnidirection microphones, since the hard boundary of the floor minimizes velocity differentials while maximizing pressure. "Boundary microphones" make use of that effect for increasing the gain particularly at low frequencies.
I don't think you can get more than 3dB in that manner but it's better than nothing.
In this video this technique is visibly used with an omnidirectional mic for "EQ-ing" the bass side of an accordion (making the low bass more pronounced without emphasizing the drone chords). If noise were an issue and the main signal of interest lower than the "hiss" you worry about, that could have helped, but if the sound source permits it (the moving bass side of an accordion cannot be captured arbitrarily closely from a stationary mic) just moving closer will increase the signal-to-noise ratio more than any such trickery can achieve.