Yes I think it would have more effect with the plastic holder due to it's low thermal conductivity, perhaps the copper wires suck away some of the heat
BTW the bare sensor equivalent is Vishay NTCLE 203E 3302 SB0
Digikey part No BC2730-ND
3,000 Ohms at 25°C
$2.37 ea
The same sensor is used for air temperature