Question Does Phenom 1055T go well with Gigabyte 880GM-D2H rev 1.4 ?

2000

That motherboard lacks a robust VRM solution. You should look at a motherboard with a heatsink over it's VRM area. Here's a shortlist;
https://www.cpu-upgrade.com/CPUs/AMD/Phenom_II_X6/1055T_(125W)_motherboards.html
but cross-reference the motherboard's and their support pages to see details about the motherboard.
 
Phenom 1055 is just about $10.
Not where I live, even when ordered from China. A 1055T is anywhere between $25 and $70 on my local eBay. A 1090T is even more expensive. Think I'll stick with my X4 955 and X4 965 builds as they are. One of my boards will take a 140W CPU. I think it has a heatpipe joining the chipset heatsink with the VRM heatsink.

Your existing X4 455 is rated at 95W TDP:
https://www.cpu-world.com/CPUs/K10/AMD-Athlon II X3 455 - ADX455WFK32GM (ADX455WFGMBOX).html

There are two versions of the X6 1055T, one rated at 125W, the other at 95W.

This 1055T is 125W:
https://www.cpu-world.com/CPUs/K10/AMD-Phenom II X6 1055T - HDT55TFBK6DGR (HDT55TFBGRBOX).html

Alternate 95W 1055T:
https://www.cpu-world.com/CPUs/K10/AMD-Phenom II X6 1055T - HDT55TWFK6DGR (HDT55TWFGRBOX).html

Assuming your existing system isn't showing signs of stress with a 455 and you don't run any long CPU stress tests, the 95W version of the X6 1055T should be OK, provided you don't increase the multiplier.

CAUTION: I cannot find the 125W version of the X6 1055T in the CPU Support list for your mobo, but it does include the 95W X6 1055T and the 125W X4 980. All the other CPUs are 95W or lower, so it's probably not worth trying a 125W 1055T. The BIOS might reject it and the VRMs could complain.
https://www.gigabyte.com/Motherboard/GA-880GM-D2H-rev-1x/support#support-cpu

If you feel brave and don't mind an unsightly bodge, you could fit some small VRM heatsinks. I did this on an old Intel board and the MOSFETs run slightly cooler. You'd need heatsinks with 3M thermal tape or use thermal epoxy. Just make sure they don't fall off and cause internal shorts. My modified mobo lies flat, not vertical.
https://www.amazon.com/Easycargo-Heatsink-Cooling-Regulators-8-8mmx8-8mmx5mm/dp/B07GN969QM

VRM heatsinks won't change the maximum current capabilities of the MOSFETs but might stop them from reaching 100°C.
 
Not where I live, even when ordered from China. A 1055T is anywhere between $25 and $70 on my local eBay. A 1090T is even more expensive. Think I'll stick with my X4 955 and X4 965 builds as they are. One of my boards will take a 140W CPU. I think it has a heatpipe joining the chipset heatsink with the VRM heatsink.

Your existing X4 455 is rated at 95W TDP:
https://www.cpu-world.com/CPUs/K10/AMD-Athlon II X3 455 - ADX455WFK32GM (ADX455WFGMBOX).html

There are two versions of the X6 1055T, one rated at 125W, the other at 95W.

This 1055T is 125W:
https://www.cpu-world.com/CPUs/K10/AMD-Phenom II X6 1055T - HDT55TFBK6DGR (HDT55TFBGRBOX).html

Alternate 95W 1055T:
https://www.cpu-world.com/CPUs/K10/AMD-Phenom II X6 1055T - HDT55TWFK6DGR (HDT55TWFGRBOX).html

Assuming your existing system isn't showing signs of stress with a 455 and you don't run any long CPU stress tests, the 95W version of the X6 1055T should be OK, provided you don't increase the multiplier.

CAUTION: I cannot find the 125W version of the X6 1055T in the CPU Support list for your mobo, but it does include the 95W X6 1055T and the 125W X4 980. All the other CPUs are 95W or lower, so it's probably not worth trying a 125W 1055T. The BIOS might reject it and the VRMs could complain.
https://www.gigabyte.com/Motherboard/GA-880GM-D2H-rev-1x/support#support-cpu

If you feel brave and don't mind an unsightly bodge, you could fit some small VRM heatsinks. I did this on an old Intel board and the MOSFETs run slightly cooler. You'd need heatsinks with 3M thermal tape or use thermal epoxy. Just make sure they don't fall off and cause internal shorts. My modified mobo lies flat, not vertical.
https://www.amazon.com/Easycargo-Heatsink-Cooling-Regulators-8-8mmx8-8mmx5mm/dp/B07GN969QM

VRM heatsinks won't change the maximum current capabilities of the MOSFETs but might stop them from reaching 100°C.
In my case TDP is 95W. Also, I don't intend to do overclock.