WiX toolset build fails after upgrading from .net 4.0 to 4.6.1: Cannot load MSBuild wrapper?

So after upgrading my whole project to 4.6.1 I'm getting this error thrown by heat when I build it:

Failed to load MSBuild wrapper object: Could not load file or assembly 'Microsoft.Build, Version=12.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a' or one of its dependencies. The system cannot find the file specified.

I also get

The command ""C:\Program Files (x86)\WiX Toolset v3.10\Bin\heat.exe" project "C:\Project\Project.csproj" -projectname "Project" -pog Binaries -gg -sfrag -nologo -out "obj\\Release\Harvested XML\_Project.xml"" exited with code 5316. 86  

The problem here is that the assembly binding log viewer is showing nothing, so I don't know where WiX is searching for the MSBuild version 12, or if it in fact exists and there's another underlying issue.

I checked a lot of SO answers and googled a lot too, but I couldn't find anything problem like this one. Of course I tried them but nothing worked.

Any ideas about this or why fuslogvw is showing nothing? That would help me a lot

Thanks a lot!

UPDATE: fuslogvw output:

*** Assembly Binder Log Entry  (28/04/2016 @ 12:28:06 PM) ***

The operation failed.
Bind result: hr = 0x80070002. The system cannot find the file specified.

Assembly manager loaded from:  C:\Windows\Microsoft.NET\Framework\v4.0.30319\clr.dll
Running under executable  C:\Program Files (x86)\WiX Toolset v3.10\Bin\heat.exe
--- A detailed error log follows. 

=== Pre-bind state information ===
LOG: DisplayName = Microsoft.Build, Version=12.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a
 (Fully-specified)
LOG: Appbase = file:///C:/Program Files (x86)/WiX Toolset v3.10/Bin/
LOG: Initial PrivatePath = NULL
LOG: Dynamic Base = NULL
LOG: Cache Base = NULL
LOG: AppName = heat.exe
Calling assembly : WixVSExtension.MSBuild12, Version=3.0.0.0, Culture=neutral, PublicKeyToken=ce35f76fcda82bad.
===
LOG: This bind starts in default load context.
LOG: Using application configuration file: C:\Program Files (x86)\WiX Toolset v3.10\Bin\heat.exe.Config
LOG: Using host configuration file: 
LOG: Using machine configuration file from C:\Windows\Microsoft.NET\Framework\v4.0.30319\config\machine.config.
LOG: Post-policy reference: Microsoft.Build, Version=12.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a
LOG: GAC Lookup was unsuccessful.
LOG: Attempting download of new URL file:///C:/Program Files (x86)/WiX Toolset v3.10/Bin/Microsoft.Build.DLL.
LOG: Attempting download of new URL file:///C:/Program Files (x86)/WiX Toolset v3.10/Bin/Microsoft.Build/Microsoft.Build.DLL.
LOG: Attempting download of new URL file:///C:/Program Files (x86)/WiX Toolset v3.10/Bin/Microsoft.Build.EXE.
LOG: Attempting download of new URL file:///C:/Program Files (x86)/WiX Toolset v3.10/Bin/Microsoft.Build/Microsoft.Build.EXE.
LOG: All probing URLs attempted and failed.

I don't know why fuslogvw is showing nothing, is it configured to log bind failures?

WiX is using the standard way to load assemblies (https://github.com/wixtoolset/wix3/blob/develop/src/ext/VSExtension/wixext/VSProjectHarvester.cs#L1119)

msbuildWrapperAssembly = Assembly.Load(String.Format(MSBuildWrapperAssemblyName, shortVersion, thisAssemblyName.Version, publicKeyToken));

The wrapper has a direct reference to Microsoft.Build (https://github.com/wixtoolset/wix3/blob/develop/src/ext/VSExtension/wixext/WixVSExtension.MSBuild12/WixVSExtension.MSBuild12.csproj#L23).

<Reference Include="Microsoft.Build, Version=12.0.0.0, Culture=neutral, PublicKeyToken=b03f5f7f11d50a3a, processorArchitecture=MSIL" />

See issue 4853 for an explanation of how heat decides which version of MSBuild to load.