@AndyR- can you clarify which bits of your existing setup you wish to replace with arduino? Do you want a replacement for the RTL-SDR dongle or is it only the PC you wish to replace? (Its not clear from your original post which bit "seems to run too hot for 24/7 operation")
Also confirm you really meant 345Mhz and not the more common 315 or 433Mhz frequencies? You have a lot less options if it really is 345.