Not much. First, most of the articles now say the so-called shortage is easing as inventory storage is starting to increase. Second most shipping companies pass the costs of fuel on to customers either as a straight line item in a bill or as a cost-plus charge, so having higher prices doesn't hurt them. It's very common to see a Fuel Surcharge on shipping bills from all kinds of freight companies. And if they bill it as a cost-plus item, a lot of shipping companies actually make money off fuel by charging their costs for the fuel plus a percentage. If they take this approach their business can become more profitable as fuel costs rise... which, not coincidentally, tends to happen when there's a supply squeeze.
Source: me. I don't know anything about this merging company specifically, but I worked for 15 years at another freight company as a software developer building their data systems, including billing systems, and just departed that job this past summer. That company did in fact take a cost-plus percentage in their Fuel Surcharge; their over-all profit margin ran from 20% under bad circumstances (slow economy, low fuel prices) to 30% under good circumstances (fast economy, high fuel prices). Done well, freight can be a reliably profitable business.