THE SHORT ANSWER
DOING IT PROPERLY
Twenty minutes and a jug of warm water fixes today. The second column is what stops you doing this every January.
Warm water, from the ground
Water temperature
Hand warm. Never boiling, it splits the pipe
Where to pour
Along the pipe, concentrating on bends and the end
Work backwards
Start at the open end, move towards the wall
Awkward bends
A cloth soaked in warm water wrapped round
Then reset
One reset once the pipe is clear
Do not climb
If you cannot reach it from the ground, call
One of these, once
Lag the outside run
Proper weatherproof insulation, not pipe foam
Increase the diameter
A wider external pipe is far less likely to block
Reduce horizontal runs
Long flat sections are where it collects
Improve the fall
So it drains rather than sits
Reroute internally
To an internal waste. The permanent fix
Trace heating
Where rerouting genuinely is not possible
DOING IT SAFELY
1
Hand-warm from the kettle mixed with cold is right. Boiling water can crack the plastic. Whatever you pour will freeze on the ground, so be careful where you stand, and do not go up a ladder in icy conditions to reach a pipe. If you cannot reach it safely from the ground, call somebody.
2
The blockage is usually at the most exposed point: an elbow, an outside bend, or the open end. Start at the end and work back towards the wall. A cloth soaked in warm water wrapped round a bend works well where you cannot pour.
3
A pipe that froze once will freeze again. The fixes are lagging the external run with proper weatherproof insulation, increasing the pipe diameter outside, or rerouting it internally to a waste. Rerouting is the permanent answer and it is not a big job.
YOUR SITUATION
First time it has happened
It happens every winter
You cannot reach the pipe
It thawed but will not restart
COMMON QUESTIONS
How do I know if my condensate pipe is frozen?
How do I thaw a frozen condensate pipe?
Can I use boiling water?
Why does the condensate pipe freeze?
How do I stop it freezing again?
It will not thaw. What now?
BEFORE YOU GO
More of the same, written by the engineers who do the work.