We present the modeling efforts on antenna design, frequency selection and receiver sensitivity estimation to detect vesicoureteral reflux (VUR) using microwave (MW) radiometry as warm urine from the bladder maintained at fever range temperature using a MW hyperthermia device reflows into the kidneys. The radiometer center frequency (f(c)), frequency band (Deltaf) and aperture radius (r(a)) of the physical antenna for kidney temperature monitoring are determined using a simplified universal antenna model with a circular aperture. Anatomical information extracted from the computed tomography (CT) images of children aged 4-6 years is used to construct a layered 3D tissue model. Radiometric antenna efficiency is evaluated in terms of the ratio of the power collected from the target at depth to the total power received by the antenna (eta). The power ratio of the theoretical antenna is used to design a microstrip log spiral antenna with directional radiation pattern over f(c) +/- Deltaf/2. Power received by the log spiral from the deep target is enhanced using a thin low-loss dielectric matching layer. A cylindrical metal cup is proposed to shield the antenna from electromagnetic interference (EMI). Transient thermal simulations are carried out to determine the minimum detectable change in the antenna brightness temperature (deltaT(B)) for 15-25 mL urine refluxes at 40-42 degrees C located 35 mm from the skin surface. Theoretical antenna simulations indicate maximum eta over 1.1-1.6 GHz for r(a) = 30-40 mm. Simulations of the 35 mm radius tapered log spiral yielded a higher power ratio over f(c) +/- Deltaf/2 for the 35-40 mm deep targets in the presence of an optimal matching layer. Radiometric temperature calculations indicate deltaT(B) 0.1 K for the 15 mL urine at 40 degrees C and 35 mm depth. Higher eta and deltaT(B) were observed for the antenna and matching layer inside the metal cup. Reflection measurements of the log spiral in a saline phantom are in agreement with the simulation data. The numerical study suggests that a radiometer with f(c) = 1.35 GHz, Deltaf = 500 MHz and detector sensitivity better than 0.1 K would be the appropriate tool to noninvasively detect VUR using the log spiral antenna.