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disortion from heating

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Many years ago I heard of a team of technicians who had developed a technique
to straighten deformed steel bridge structures  in place by flame-
To help me understand the principles, this is my question:

Assume a steel plate say 3/8" thick by 4" wide and 3 ft long, simply supported
at the ends, say resting on a pair of saw horses.   Heat is applied across the
top at the center, for example by welding a 1/4 x 4 " wide gusset plate at the
center, across  and perpendicular  to the plate ( 2  3/16"  f illet welds, 4
'' long , for example)  .

Will the center of the plate rise or will it sag ?  In another form, the
question is which will prevail -  The loss of rigidity while the top is molten
or the contraction effect upon cooling?