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We study the entanglement entropy (EE) and the R\'{e}nyi entropy (RE) ofmultiple intervals in two-dimensional $T\overline{T}$-deformed conformal fieldtheory (CFT) at finite temperature by field theoretic and holographic methods.First, by the replica method with the twist operators, we construct the generalformula of the RE and EE up to the first order of a deformation parameter. Byusing our general formula, we show that the EE of multiple intervals for aholographic CFT is just a summation of the single interval case even with thesmall deformation. This is a non-trivial consequence from the field theoryperspective, though it may be expected by the Ryu-Takayanagi formula inholography. However, the deformed RE of the two intervals is a summation of thesingle interval case only if the separations between the intervals are bigenough. It can be understood by the tension of the cosmic branes dual to theRE. We also study the holographic EE for single and two intervals with anarbitrary cut-off radius (dual to the $T\overline{T}$ deformation) at anytemperature. We confirm our holographic results agree with the field theoryresults with a small deformation and high temperature limit, as expected. Fortwo intervals, there are two configurations for EE: disconnected ($s$-channel)and connected ($t$-channel) ones. We investigate the phase transition betweenthem as we change parameters: as the deformation or temperature increases thephase transition is suppressed and the disconnected phase is more favored.

Entanglement and R\'{e}nyi Entropy of Multiple Intervals in $T\overline{T}$-Deformed CFT and Holography