The specific question seems to be asking about takeoff in rain and then temperature drop affecting the "wet" wing, rather than icing at altitude.
A common rule is that an aircraft is considered to be in "icing conditions" if any of:
a. on ground, OAT 5 deg C or lower and "visible moisture" - which could be clouds, rain, mist, snow
b. in air, TAT up to 10 deg c, visible moisture as above
c. ice detection system detects.
Under CERTAIN circustances, (c) can override (b) i.e. if (c) says "no ice" and (b) says "maybe ice", then you can assume "no ice". In other cases you have to go with the more conservative, if either says "ice" you assume "ice"
However, all of those are intended to cater for direct ice accretion on the aircraft i.e. you're flying along and start to accrete ice on what may have been a dry wing.
For the case of a "wet" wing, if the takeoff is near freezing, you are at significant risk of ice forming; hence the 5 deg C typical limit up to which you'd assume icing conditions prevailed. If you take off in a summer rainstorm though, the chances are that if you clear the rain before climbing too high, so that you have a "wet and warm" wing, the water will almost all blow off in the airflow; after all, a so called "running wet" anti-icing system leaves water on the protected surfaces, which does exactly that. So for the SPECIFIC case raised, the risk of icing is low to nil.