Lots of smart guys on this thread, and they are probably right about the heat issue being the primary issue.
So yeah check for DC, check for polarity, etc.
But I wonder....
A 1646 replaces a 1:2 transformer not a 1:1 transformer because the 1646 adds 6db ( or 5.3dB into 600 ohms)
Furthermore, a transformer sees an unbalanced load and a balanced load and treats them identically. A 1646 does not.
Furthermore a transformer treats a hot signal on the primary "gracefully" (you can make it distort but transformers don't clip) but a 1646 will half the output if you drive unbalanced.
So are you driving a oscilloscope with one side connected to a grounded ground clip?
So what are you driving with this thing (during your test). Is it driving unbalanced or balanced? what is the load?
I suggest you tell us a bit about your test environment and the actual test values. Rather than expressed in terms of gain, expressed in terms of RMS Volts or dBu of output. Tell us what load you are driving. The power rails would limit the output dBu to an unbalanced output (one side shorted) to about 25 volts RMS (30dBu). The same test into balanced would double the output.
from the 1646 datasheet.
Gain structure
The 1606 and 1646 both provide +6 dB gain
(factor of 2) between their inputs and differential
outputs. This is appropriate, since with a balanced
output, twice the voltage between the power supply
rails is available at the output of the stage. The
single-ended input of the 1646 can accept signals
that swing to nearly the power supply rails without
distortion, when driving into a differential (floating)
load. The balanced input of the 1606 can accept
signals at each input that swing to nearly one-half the
power supply rails without distortion, when driving
into differential loads.
Both devices, when driving single-ended loads,
will clip at about half the output voltage as compared
to a differential load. This is because only one of the
two output signals will be available. Despite the
output clipping, the input to the devices does not
need to be constrained - they will work without
undue problems being overdriven at their inputs
when the outputs are clipping into single-ended
loads.