That's odd. From my perspective, an ideal transistor has zero temperature sensitivity across the linear range, zero voltage drop across the PN junctions, a beta cutoff frequency of infinity Hz, 0 ohm stray base resistance. Oh, and doesn't overheat.
I think OP meant "An ideal MOSFET". :)
That would be somewhat unfair towards MOSFETs and their quite versatile spectrum of applications though: MOSFETs are actually also being used for lots of linear applications. For high power linear stuff, they have to be designed slightly differently than cheaper MOSFETs designed solely for switching, so as to not run into ETI (electro-thermal instability) problems, but it's not uncommon. So, maybe "an ideal transistor for switching/digital purposes"?
OP might be closer to "an ideal solid-state relay"