Antenna Cable Setup 300ohm vs Coaxil cables

Our out doors antenna uses 300ohm twin lead connections. Would coaxial cable connections make any difference? Right now I have the antenna cable running to a splitter box that splits into 3 300ohm-twin lead cables connected to 2 TVs and 1 computer. This splitter box was made for taking 1 lead and turning it into 2 but I’m using it for 3. Figured i might get a new coaxial splitter from Trisonic that is sold in the $1 stores which turns 1 to 4 so each would have it's own decanted coaxial connection. The 300 ohm antenna cable would be connected to a coaxial adapter like VCRs come with to the new coaxial splitter. Then i would be using Trisonic RG-59U coaxial cables also sold in the $1 store to connect all the TVs and computer. One question does the splitter ever get hot since this will be screwed to the floor joints in the basement? I'm thinking of changing to this new cable setup since in the beginning setup worked fine but for some reason some channels have started to come in snowy months ago and effecting channels reception on different TVs. The computer is using a PCChips TV tuner card in a dell P3 500 MHz with 512SD100Ram.