As alluded to by earlier posters, there's no simple solution, the temperature rise is not linear, but exponential. The formula for temperature rise depends upon Static Temperature (SAT) and Mach Number, but, as these two inputs yield TAS, the formula may be much simplified by directly applying TAS......
Temperature Rise = (TAS / 87.1)^2 (For Temperature in Celsius, and speed in Knots)
If you're looking for the FIRST 1 degree rise, for an aircraft accelerating from zero speed, that will occur at 87.1 Knots TAS (100.2 MPH for those who live in the olde worlde).
Being exponential, further 1 degree rises will occur at decreasing speed increments, e.g.
+1 Degree at 87.1 Knots
+2 Degrees at 123.2 Knots (a further 36.1 Kt)
+3 Degrees at 150.9 Knots (a further 27.7 Kt)
+4 Degrees at 174.2 Knots (a further 23.3 Kt)
+5 Degrees at 194.8 Knots (a further 20.6 Kt), etc, etc....
As we approach typical jet aircraft cruising speeds, it requires a TAS of 477.1 Kt to achieve a Temperature rise above Static of +30 degrees, to achieve +31 degrees requires a mere additional 7.9 Kt TAS, increasing temperature rises require much decreased speed increments).
Strongly recommended that testing on the M1 is limited to a +1 degree temperature rise!!!!!!
Regards,
Old Smokey