In order to improve the frequency-division multiplexing (FDM) in transition edge sensor (TES) imaging arrays, it is suggested to replace commonly used SQUID amplifiers with a semiconductor high-frequency cooled amplifier. This would result in a single 10-GHz bandwidth amplifier serving the array of more than 1000 detectors. The basic idea is to implement an antenna-coupled TES as a load for a high- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> resonator, weakly coupled to a microwave transmission line. This high-frequency scheme substitutes the traditional wire connections to the TES. The NEP as low as 2×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-19</sup> W/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</sup> is estimated at ambient temperature of 300 mK for submicron-size TES absorber made of Ti; the NEP is limited by 3 K noise temperature of the amplifier. To verify the new concept, prototype TES devices made of Nb are developed and tested above 4 K. The NEP of about 1.5×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-15</sup> W/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</sup> is estimated for the experimental micron-size prototype devices made of Nb at 4.5 K. The <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">IV</i> -curves of the TES at different temperatures are recovered using the RF and heat balance models along with the experimental <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ) data; presence of the negative electrothermal feedback is verified.