Is it safe?

Depends on its circuitry and what sort of filtering and regulation it has. It MAY be okay, but then again it may not. Consider that accelerated life tests sometimes stress unit with higher applied voltage and higher temp.

Unless the modem is marked to say that it can accept that voltage, then yes, there is the possibility of damage. It might not happen all at once, it might destroy the modem over time. I certainly wouldn't do it unless I was planning to buy a new modem soon anyway.

Cheers, Nicholas Sherlock

In all likelihood, what's happening internally is that there is a voltage regulator which is running noticeably hotter than before, and is coping OK for now. Probably the whole thing will age faster than before, or it might just go pop one day.

OTOH I've had some cheap far eastern network gear which was sometiumes delivered with 9V and sometimes with 12V supplies, and the 12V versions ran far more stably for a long time.

If it works, and it's a cheap router, use it. If it goes pop, buy another one.

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Pop it open, trace the power circuit, see what the parts in it are rated for. You didn't mention whether either adapter was regulated or not, and what their current ratings were vs the rated power consumption of the modem instead of just peak requirement, which if you're lucky will be in it's manual and somewhat accurate.

I Don't know - is it safe? Hindu

It will be OK until it stops working.