The coldest part of the A/C system is the expansion/oriface valve. If the system is left without gas in it for any length of time then it can fill with air. Air contains water vapour.
If any water/water vapour isn't properly purged (vacuumed) from the system before being refilled, then the water/water vapour can freeze in the expansion valve and effectively bung the whole system up. This causes the pump to work hard pressurising the coolant into the HP side, but if there is no flow of gas around the system, then all that happens is the gas gets hotter and hotter. The pump has an overpressure cut out, so it may well deactivate itself if this happens, till the ice in the expansion valve melts again. I think the expansion valve is in the cabin behind the dash on an Omega B?
There is a dryer in the system too - it's part of the A/C rad on an Omega - that bottle shaped canister on the front nearside of it. This contains a sort of silica gel, and it's job is to try and capture any moisture in the system. This should not be left exposed to atmosphere for too long before re-gassing because it will capture moisture from the environment. I assume your new rad came fitted with a new dryer? Mine did.
The pipework down the passenger side of the engine on my car (3.0 24V RHD saloon) is ice cold within 10 seconds of starting the engine - too cold to hold onto for very long.
ETA : Just remembered - I've got a digital thermocouple widget in the boot

. The LP pipework (where the LP valve is) measured +5 DegC. The HP pipework (out of the compressor near the HP valve) measures 55+ degC. Ambient here is around 20 DegC today.