First, just putting a relay at the transformer secondary will not work well enough. The relay will close in a split second after power is applied, before the surge current has a chance to settle down. You need a delay of at least a few seconds, which requires that you add some delay circuitry to close the relay, or use a special time-delay relay.
Second, thermistors work by varying its resistance with respect to temperature. The idea is to use a NTC (negative temperature coefficient) thermistor so that immediately after power is applied, it inserts enough resistance to absorb the current surge, but as the thermistor warms up due to the load current, its resistance will drop to reduce the current limit.
Assuming that the application is for a high-power audio amplifier, the problem is that you need to pick a thermistor that would get hot enough under the desired load to drop in resistance, and hopefuly it would go as close to zero as possible so it doesn't become a current bottleneck. The fact is you'll have a hard time finding one that has enough resistance change that would give you a large enough current limit at turn-on and still get close to zero ohms (after all, the way thermistors work is by having some resistance. and the voltage drop on that resistance multiplied by the current draw is what causes it to heat up).
To complicate matters, unless you're talking about a pure class A amp with steady-state current draw, class AB amps draw very little current while idle, but could change to many amperes based on the music signal (depending, of course, on the power output of the amp and the connected speaker load). So the thermistor will cause the AC voltage (as seen by the power transformer primary) to fluctuate according to changes in current draw. Not a good thing! Plus it would further complicate the selection of the thermistor -- you need to select one based on the maximum current draw, but then at idle it probably won't get hot enough.
If you're going to implement a relay to short out the thermistor after some delay, then why bother with a thermistor at all? Just use a standard power resistor, let it absorb the surge, then have the relay disable that resistor and be done.