A Vinyl LP is Thermoformed and the composition of the material will react to heat and deform, as well as conditions that are applying force to a degree that can cause it to deform in shape.
Methods to correct a deform in shape can utilise both of the above influences, the use of Heat and Force are the common methods chosen. The not so common method chosen is Force only and relying on a ambient temperature as the heat source.
Methods to flatten a Warped LP are around for a very long time, and were probably presented as a method from an era, when a LP that was deemed as a damaged and very easily replaceable due to the LP as a commodity being readily available, the Flattening Devices in their earliest concepts were one of many other marketable product, offered as a ancillary device, most likely to be purchased by individuals with a desire to 'make do and mend'.
The times have changed and the Vinyl LP is not so readily available, and the need to 'make do and mend' is a genuine consideration. The LP as a commodity today is for certain Albums a thing of rarity. If such a rarity is to receive a corrective treatment, the rarity, put a new emphasis on the considerations that are required to ensure the correction is not detrimental to the LP in general.
The only real concern that should be in place, is whether the outcome of a Groove having deformed and them being deformed once more, to be returned to an earlier shape, will have incurred an unavoidable change to its form produced at the time of the pressing being new.
A Thread on another Forum has covered this subject and has suggested a variety of methods using Polished Edge Glass Sheets as the press to supply the force.
The Methods are all reported on as being successful, but in my mind some are carrying more risk than others and there are not guarantees, one method using force applied heat can be replicated in another set up.
One individual used the Glass Sheet Press with a added Weight only, and had reported that the LP was flattened within a month.
This as a method, in my mind is the method that presents the least risk for the LP, as there is not a force heated environment being created, where forced heat or point source heat is presenting an additional risk.
The time required using the Press/Force only method, could probably be decreased if the materials were placed into a smaller environment with an increased Temperature set with a range between 25 - 40 Degrees Celsius, with 40 as the maximum.
In my mind the temperature should be ambient and not created by forcing or applying heat directly to a press material that is being used, as this could create a point source for the heat, and the LP could be detrimentally impacted on as a result.
A method to control the temperature to a chosen level of heat, could be achieved at e very cost effective outlay.
A Polystyrene Box used for Temperature Controlled Transportation, with a Herpetologist's Heat Mat placed inside will be a very suitable method.
A Heat Mat produces a uniform heat over the mats surface, so a hot spot is not radiated, creating an intensely heated zone, using the Heat Mat with a Thermostat will be ideal for producing a very cost effective method for controlling the Box's evenly distributed Temperature with a low voltage heating device.
I had a unwanted experience once when using a Oven to be the source of heat. , When trying to make a form in a foam material, the Foam was placed and concealed, between two heavy metal plates and the Fan Oven set to a low Temp'. The low Temp' was still able to create a Hot Spot, which caused the foam edge to deform to a non correctable condition.
I don't recommend using an Oven as a method for rare vinyl LP's, I don't see how a condition can be created that is reliable and consistent for all adopters of the method, unforeseen risks seem inevitable.
For the DIY Method and not using purpose produced devices, the Ambient Room Temp and Press with applied weight, with an allowance for the time needed to complete the reforming of the original shape, is looking like the best place to begin.
If a version of this method is then wanted which can potentially produce a decreased time requirement for the process. The method to produce a space with an increased ambient Temperature being present, seems to be the next method that has the least risk attached.