13,500 BTU rooftop

I don't understand your question.

I'm guessing here but it looks like you are running it on an extension cord and standard wall receptacle. I have run my 15,000BTU off of an extension but be mindful of possible heat issues where they are plugged in and that your voltage coming in is no lower than 10% of 120V. Possible fire hazard? Low voltage is not good for any appliances.

trailer's electric 30amp cord has an rv adaptor on it for 110. The electric outlet is less than 8 ft. away from fiver.

I've been checking the adaptor and cord throughout the day for excessive heat...cord is cool.

I'd like to stay in trailer tonight as house has no air conditioning.

Your TT's plug is 110 with 30 amps available. As long as the voltage stays up (which it should unless the electrician did something wrong) you can run the AC indefinitely.

I don't see the problem?

Is the socket you are using on a gang? Is your voltage dropping? To what?

I would convert both/all connections to the 120VAC twistlock type. Firmer, more safe, connections.

To the OP, I've done the exact same thing with my old trailer with 13.5K air off a 15 amp circuit in the garage with no problems. A 20 amp circuit would be better if you have one available. I later put the 30 amp plug receptacle in.

I have abandoned our non air conditioned Portland house on occasion and used our RV. Plug into outlet that doesn't have any major draws .. monitor voltage from inside the RV and if it drops to less than 109 turn off the air conditioner .. make sure your batteries are already charged or turn of the converter (combo of converter and air conditioner may overload system) and put your refrigerator on gas vs electricity. If you have to add an extension cord the shorter and thicker the better. I have been told that having clean condenser and evaporator coil is suppose to reduce amp draw - if true that would help.

$310 for a Progressive Industries EMS-PT30C, or $258 for the EMC-LCHW30C hardwired in, and all these worries will be history. Your A/C will run, or if there is an undervoltage, the EMS will shut things down to protect the compressor from burning out due to low voltage.

Caveat: Make sure the electrician is installing a 30A, 120VAC connection. I've read about way too many fricasseed RVs when they end up with a "dryer outlet" that has two 120VAC hots and a neutral as opposed to a hot, a neutral, and a ground.

In fact, if you are getting an electrician to install a pedestal, might as well go for a 50 ampere pedestal with a 50 amp, 30 amp, and a 20 amp series of receptacles. In the scheme of things, this won't be that much more on top of the exiting electrician costs, but you will gain a lot more functionality.