Yes, it is plausible as the timescales of which a red dwarf is a blue dwarf are quite big, to the point where if your icy planet is distant enough it will thaw and potentially develop life. What matters is the placement of your planet and its size, as if your icy planet is too small it won't retain a atmosphere and if it's too far the temperature increase will only make the planet only go from Triton cold to Europa cold. There are exoplanets with substantial amounts of water whose origin comes from a icy planet that migrated inwards. They are worlds with world spanning oceans and very thick atmospheres of vapor. Your world, being a world that thawed will get its atmosphere from when its icy surface slowly melts away. Since water vapor is lighter than nitrogen, your world is likely going to be bigger than earth to retain its atmosphere.
The biggest concern for your world I see comes from geology, as with such a ancient planet the geological processes within the world likely have died down after trillions of years. This may actually inhibit life because of the role geological activity on earth played in the origin of life, and may play on other worlds like Europa if there is hydrothermal vents on Europa. 258
You likely could circumvent this issue by having life actually form extremely early on in the red dwarf's life when your world is geologically active, but be frozen or evolutionarily static for trillions of years due to having no incentive to evolve. (This does happen on earth in certain instances, such as with the Coelacanth who were thought extinct yet still are around, in a much simpler, far less biodiverse ecosystem, life not advancing beyond simple organisms like bacteriums for trillions of years may actually be possible). Your life is likely to be radiation resistant, because being around a red dwarf exposure to higher radiation levels is a given. This is good news for your life as a ancient world trillions of years in age is going to be geologically dead no matter what the size of your planet. One possible way to circumvent this is by having your world part of a binary planet system (and therefore gets geological activity from tidal stress, a process that is seen around pluto).
A civilization may well develop, they have the time and evolution being the fickle and semi-chaotic thing it is on a world with rocky landmasses mixed with water has the potential for intelligent life to develop. However, if they are a space faring society they'll be going a very different tech path than on earth to get there because they'd lack access to fire due to a water vapor atmosphere and without geological activity they'd also lack access to any form of volcanic metallurgy. You should consider inventing creatures that can circumvent this issue somehow, perhaps through intense body heat. They may take far longer to develop a space faring civilization than per say, a world like earth might, but since they have hundreds of billions of years they have more than enough time to figure things out.
Further Reading:
http://abyss.uoregon.edu/~js/ast121/lectures/lec15.html http://www.solstation.com/planets/water-worlds.htm http://m.space.com/6560-life-thrive-red-dwarf-star.html http://iopscience.iop.org/0004-637X/673/2/1160/pdf/0004-637X_673_2_1160.pdf http://es.ucsc.edu/~fnimmo/website/Triton.pdf 258