Check your radiator has coolant in. I'm gonna bet the garage have drained your rad to do the work and forgotten to put fluid back in...
The fans won't come on if the rad isn't hot and the rad won't get hot if its bone dry!
Whilst the car is cold, pop the bonnet, and open the radiator cap. Look inside and fluid should be over the top of the rad elements and maybe even some coolant in your overflow reservoir (if the RX300 has one). If you can't see any and you don't have any coolant at home, fill the radiator up with tap water as a VERY short term measure and take it straight to the garage where they can drain it and put OEM spec coolant in.
If there is coolant, the next check would be the thermostat if it were mine.
If its the former, get them to sort it free of charge and then sack them. Take it somewhere else next time because thats a schoolboy error!