REBa2Cu3Oy (REBCO)-coated conductors (CCs) derived from the Trifluoroacetates-Metal Organic Deposition (TFA-MOD) process are expected to be used in power applications since they are low-cost and provide high performance. For low-cost production of reel-to-reel system TFA-MOD REBCO CCs, a high rate of productivity during the conversion process is necessary. The heating rate (RH) during the steps required for conversion is the key factor for realizing a high rate of productivity. In this study, in order to investigate the influence of RH on microstructures and superconducting properties during the conversion process, we fabricated TFA-MOD (Y,Gd)Ba2Cu3Oy ((Y,Gd)BCO) films on SrTiO3 substrates using different RH. The (Y,Gd)BCO films with low RH (< 15C/min) showed a low self-field Jc(Jcs.f.) due to the formation of a-axis-oriented grains. On the other hand, the films with high RH (> 25C/min) showed a lower Jcs.f. because of the formation of non-superconducting phases (Y and Cu-poor). We found that the film fabricated with RH= 20C/min has high crystallinity, as well as a high Jcs.f.=4.3 MA/cm2 at 77 K compared to those of other films. Optimizing the RH during the conversion process plays an important role in improving productivity as well as the Jc for TFA-MOD CCs.