Profiling a lab

It is feasible to make an ICC profile for a lab's output. I've done it.

But as Digitaldog wrote the Lab has to cooperate and the line has to stay consistent. 

Maybe test a few labs until you find one you like.

Of course if your own display screen has a bluish tint then an accurate print WILL look too warm compared. 

I use this Adobe RGB testimage - you can convert to sRGB if that’s what they specify, many labs fun such as Fuji Frontier and that accepts only sRGB. 

Want to be sure all the ducks are in a row? 

Have you ever wondered how to KNOW whether your screen [or printer] is ACCURATE and not just 'pleasing'?
If so please check this out: http://www.colourmanagement.net/products/icc-profile-verification-kit

I hope this helps
neil barstow, colourmanagement net :: adobe forum volunteer:: co-author: 'getting colour right'
google me "neil barstow colourmanagement" for lots of free articles on colour management

Without direct input and cooperation, this isn't going to fly. 

First, they MUST output the color targets with no color management, any automatic corrections or anything that would affect the output day in and day out. A profile profiles a fixed condition. If the conditions change, the profile is invalid. 

Next, the lab must accept the image data you then send, converted to that output profile; will they or do they demand something (ugh) like sRGB? 

Best you might be able to do, and this will only work IF the output is consistent day in and out is make a layer adjustment to address the tad warm output and use that on top of your sRGB or whatever RGB Working Space document to adjust to this bias. But a profile you make? Very unlikely.