TRMM data are usually delivered in a specific HDF format which is (partially) supported from GDAL 1.8+ (so,would in theory work).
However, it is easier to get binary grids from here
The format is explained here. Hence, to import gridded TRMM into a Lat-long location with is done via
# generally r.in.bin -f -b north=50 south=-50 east=180 west=-180 rows=400 cols=1440 ....
r.in.bin -f -b input=3B43.100101.6.precipitation.bin output=3B43.100101.6.precipitation \ north=50 south=-50 east=180 west=-180 rows=400 cols=1440
Optionally convert then to mm/hr to some other time unit.