For the material parameters of Sapphire at 300K, the TE and TR Noise profiles, though not very close, lie close to within an order of magnitude. Sapphire has a positive coefficient of linear expansion. We just inverted the sign of this quantity
and the ran the codes that puts heat and pressure simultaneously to the test mass. The total noise looks to be lower than the TR noise which is greater.

Mirror radius 0.25[m]

Mirror height 0.46[m]

Beam Radius 0.09[m]

If we have physical parameters which make the two Noise sources come closer to each other and then flip the sign of alpha, we may be able to see some noise reduction to a greater extent.