The proposed sensing device relies on the self-imaging effect that occurs in a pure silica multimode fiber (coreless MMF) section of a single-mode-multimode-single-mode (SMS)-based fiber structure. The influence of the coreless-MMF diameter on the external refractive index (RI) variation permitted the sensing head with the lowest MMF diameter (i.e., 55 μm) to exhibit the maximum sensitivity (2800 nm/RIU). This approach also implied an ultrahigh sensitivity of this fiber device to temperature variations in the liquid RI of 1.43: a maximum sensitivity of -1880 pm/°C was indeed attained. Therefore, the results produced were over 100-fold those of the typical value of approximately 13 pm/°C achieved in air using a similar device. Numerical analysis of an evanescent wave absorption sensor was performed, in order to extend the range of liquids with a detectable RI to above 1.43. The suggested model is an SMS fiber device where a polymer coating, with an RI as low as 1.3, is deposited over the coreless MMF; numerical results are presented pertaining to several polymer thicknesses in terms of external RI variation.